As the page is about to be displayed, capture the text (probably, basically a large string) using a code hook.
Use the same memory allocation functions the target is using (if it's using a DLL CRT it will be easier).
"Realloc()" or just recreate the text to fit in your changes (I.E. an html button section) using string functions.
The hard part might be that you'll have to handle the extra button press(es) your self via probably yet another hook.
Is it connecting to hosted webpage on the net?
If not it probably has a mini-webserver built in. There is a good chance in this case it's either using an open source, or commercial setup. Look for strings in the target that indicate what library/system it might be using, and, or, look for relevant DLL's (like "awesomium", etc.) in the targets path. You might be able to find matching libs that you can use; again making some general assumptions that you are going to facilitate your mod/hack via a DLL.
You got to do more RE'ing to find out how it's doing things and the answer(s) will reveal it's self.