Here is an example
The image isn't mine, I just grab the firs appeared to be good as an example of the topic issue.
It's not particularly easy to remove entirely because where there are sweat stains there are also generally a lot of texture. I would probably try masking the area (making a layer that covers the area of the stain) and then use that mask to brighten the image up and make the stain less noticeable. I'd 'also probably feather the edges a bit to help blend it in as the wet spot tapers off.
It's still not going to be 100% perfect, but should make it less noticeable. It's also still a reasonably challenging thing to do a good job at without making either a dark ring or a light ring around the outside of the stain.
What you need is the High Frequency Separation technique. Then you will be able to edit the sweat spot on the low resolution image very easily, basically a color replacement, and keep the textures of the T-shirt. You just have to select the proper filter frequency (or pixel blur, in other words, in the described technique).
Do not forget to increase the color bit depth to 16 bit when you start, otherwise you will quickly see color banding.
The other way is just to paint over. With a bit of skill, you can do it with a mouse (... well, I can do it, so you can, too ;-), although a tablet and pen makes this easier (or harder, depending on your skills...).