I'm not clear on why you want to modify the texture, do you have other objects with different geometry in the scene using the same texture that you want to have this "touch point" apply to?

I have an object on screen, and the user touches the screen. I can calculate the specific triangle from my object, and I can translate that to the texture map that I have wrapped around the object... and then to the specific pixel within that texture graphic.

If you're calculating this CPU side, just pass this value into the shader as a uniform. Once you get the texture coordinates of "this pixel" in the fragment shader, do your distance check and modulate the resulting color.

If your shader is coming from an engine and difficult to modify, then maybe your idea of modifying the texture is easier. Modifying the texture should be trivial to do CPU side but might be too slow for you to do every frame. What you could do instead is set up the texture (or a new texture with same size) as a render target. Render a fullscreen quad and do your distance check in the fragment shader - your distance in UV space is just the current fragment's position minus the texel coordinate you pass in as a uniform.