Why do my TF2 sprays look low-res ingame?

Based upon the rest of how the graphics look (looking at the texture of the floor and of the wrench), it may be your graphic settings. It's just the way the game handles settings all around. Think of it this way, it applies a generic "template" of how to handle all graphics at certain settings. If you can up your video settings it should look a lot better.

Your spray imported as a BMP looks fine on higher settings:

I'd start by converting the image to a texture yourself, rather than relying on the game. You can use VTFEdit or Paint.NET and Nem's VTF (Valve Texture Format) plugin.