If they wanted to edit the HTML for some reason, it's trivial to just use their own image or replace the <img> with their own text.
The prevention for this isn't to render texts as image, but not to screen share your computer with random people online, much less hand mouse control over to them while you're logged in to your bank. If it's some elderly person doing this or the such, you should really teach them better or they'll get scammed from much less esoteric threats :(