How to tell speakers that their English is terrible?
I think that your plan is based on number of possibly wrong premises. And even if they were mostly right, I doubt such a plan could have any reasonable success. Let's see my reasons.
I just had a lecture from someone who has been a senior scientist (and has completed a PhD, post-doc) at a hospital for already 15 years.So I'm assuming this person is experienced in giving talks in English.
I've met along the years many senior researchers, even native English speakers, who where definitely not experienced in giving talks, at all. If academic researchers are frequently experienced speakers because, at least, they have teaching duties, some researchers from research institutes are really "lab rats" who rarely deliver talks. To give you an example, a few years ago I was attending a poster session in a conference and I told one of the presenters (a native English speaker) that I was surprised that his work had been accepted as poster presentation and not as an oral one. He told me that it was actually accepted as oral presentation, but he asked for a poster one because he doesn't like to deliver talks.
My impression is that the talk was a waste of time for the two dozen people present.
Talks can be a waste of time for other reasons than terrible language: slides with unreadable results, talk targeted to the wrong audience etc. I certainly attended many talks that could be considered a waste of time for almost anyone in the rooms, and a large fraction of these talks were delivered by allegedly experienced speakers.
Now I wonder if the speaker is aware of this problem, my guess is no
In my experience among non-native speakers of English, most of the people is well aware of their level of English and of their pronunciation: your guess is likely wrong.
I feel the need to bring this to the speaker's attention.
Would you feel the same need if the talk were a waste of time for any other reason? And note that preparing readable slides is usually much easier than fixing pronunciation. And are you planning to do such an action for all the useless talks you will attend in your life?
I feel the need to bring this to the speaker's attention.
As I said, the speaker is probably well aware of this issue, but can you offer any solution that the speaker is not already aware of?
Improving pronunciation is not something that can be done easily, especially if one is not keen on languages. The speaker might have had good reasons for not having been able to improve pronunciation more than that. Time and money can be two of them. I don't know how many languages you speak -- you speak more than one, right? I speak Italian, my native language, English and French. My level of English is decent, but my level of French is basic. I cannot make great conversations in French, just short sentences, and sometimes I've been misunderstood (e.g., I once asked for a book called Rue des Maléfices and the clerk searched for Roue des Maléfices). I'd love to improve my French pronunciation because I spend most of my vacations there but, guess what, I really cannot find the time to do this. Or I'd like to learn German, because I have many German colleagues and I also found some nice physics book in German that I'd like to read without Google translator. Again, I cannot find enough time to learn German even at a basic level.
To conclude, don't.
This might be productive in a direct conversation, if you are able to establish rapport, and if you can steer the conversation in a productive direction. You could start by asking her to clarify some key point you were interested in. Stop her as soon as there's something you don't understand, and if necessary ask her to spell the word you don't understand. The goal at this point is to succeed in communicating with each other.
If you are able to accomplish that, then you could say
Thanks for clarifying that point. That is really interesting for me. I didn't understand what you said on that point during the lecture -- to tell you the truth, I was only able to get the meaning of some of what you said, and that made it hard for me to follow the arc of the presentation. I'm not very good at understanding
nonstandardunfamiliar accents. So I have to rely heavily on the visual with a lot of speakers. Your slides about (topic B) helped me a lot, because they had a lot of detail.
That is a conclusion that helps the speaker move forward in a positive direction.
Additional notes.
Often one needs to crank up the belief in oneself in order to get through the PhD and other hurdles in academia. This sometimes leads one to a slightly Aspergeresque attitude of "I can find the words I need to express myself; mission accomplished; I'm not interested in how well other people are understanding me." Step one is to establish rapport.
Sometimes this rapport can result in the stronger English speaker having some influence over the other. Sometimes it results in the stronger English speaker getting tuned into the other's speech patterns better, and perhaps also developing empathy for what has led the other to his or her current state of mediocre English. This happened to me with respect to my advisor. For the most part I'm one of those people who finds horrible English, or horrible French, or horrible Spanish, excruciating, like chalk going the wrong way on a blackboard; and it continues to torment me later like a stuck song (ear worm). Once my empathy with my advisor was established, certain patterns, such as his tendency to omit words, got a lot less on my nerves.
Today I had a brainwave. If the speaker's English is that bad, the hosting department should provide an interpreter.
Don't send the email. Based on my experience, I predict that the anonymous email you are proposing to send almost certainly won't tell the speaker any information she does not already know, only something that she is either in denial about or that she is (for whatever mysterious reasons of human psychology) helpless or unwilling to do anything about. On the other hand, especially due to its anonymous nature, the email is quite likely to come across as hurtful and to cause her negative feelings such as guilt, self-loathing, low self-esteem, depression, etc., that would make her situation worse without leading to any progress towards resolving her accent/language problem.
There is a time and a place to offer people negative feedback that might help them improve, e.g., when such feedback is directly solicited from you or when you are a person whose job it is to offer such feedback. That time and place is not your current situation. So don't.