Whether to accept co-authorship for conference presentation after making only a small contribution?

My answer is based on experience in the field of applied mathematics. I'm assuming (as stated in the question) that there is no written publication involved -- just a talk.

Don't worry about claiming unmerited credit

You have made some contribution. Coauthorship on a conference presentation carries almost zero significance for purposes of evaluation. It's not something you list on your CV, no matter how "early career" you are. Usually, if you are not already well-known and the results are not earth-shattering, then nobody will even remember, five minutes after the talk, that you were a co-author.

When to insist on being removed

Obviously, coauthorship of the talk has some significance to you and to the presenter. Since the presenter has already made it clear that he wishes to include you as coauthor, I would only insist on being taken off if:

• The scientific work or the quality of the talk is so bad that you think it will reflect negatively on you; or
• Your involvement is so minimal that you couldn't say anything interesting about the project (if asked by someone who attended the talk).

It doesn't sound like either of these conditions apply, so my advice is to let it go.

I am relatively new to science so my answer is from a perspective of a young scientist. It seems to me you contributed enough to be one of the authors so you certainly can be included. Sometimes a beginner can spend months working on something and accomplish less than an experienced scientist can contribute within a few minutes by a good comment or suggestion. Ultimately, it is the results that count, not the amount of time and effort spent.

If you also happen to be an expert in what the conference presentation is about, then you should be included as one of the authors. On top of acknowledging your contribution to the research, it tells everyone that there is another scientist out there who knows a lot about the particular subject. Other scientists and students can then contact you for advice, recommend you as a reviewer, or even choose you to be their PhD supervisor. So excluding yourself from authors may also seem a bit unethical as hiding your expertise from the world.