Interfacing Android App to make WordClock-like Timer

Hi all!
I'm learning the Arduino and have an idea ... i'd like to make a large 7-segment timer for my homegym ... put they're expensive.

Instead, i'm planning to make a word-clock-like timer, something like this. It'll be cheaper, but more importantly to me, fun to make a custom to what I want.

I already use an app on my Android to track my workouts and that app has a button that lets you track when you're done with a set.

Here's the tricky bit to me ... since this app doesn't have an API (not that I've ever used one before, either), what would be the "best" way to scrape the screen when I push the button to mark the set as "done"? Once that's been done, I can then send that to the timer using some already implemented ways (bluetooth for example) ... and can keep using the app with all of my workout data.

Any suggestions?

Thank you!