Peter,
Thanks for getting in touch! We definitely discourage users from editing the plugin files directly because of the reason you mentioned above. You’ll notice that almost all of our functions are filterable, so you should be able to modify the output of the function by using the filters that we’ve provided. If you look at ‘tribe_events_the_previous_month_link()’ you’ll notice that there’s an ‘apply_filters’ reference at the very end of the function. This is so that you can write some code to customize the output if you’d like.
Pasting something like this into your theme’s functions.php file will get you started: https://gist.github.com/ckpicker/4d570fb29217df9ca603
Of course, you’ll have to write all of the logic to parse the HTML string and modify as needed, but that should get you started in the right direction. Good luck, and let me know if you have further questions! 🙂
-Casey-