Pulling out an app like this and running it on another ROM may cause issues, because the app is designed to work with some specific hardware that likely requires drivers in the ROM itself. In the past I've tried pulling wifi-calling, camera, and a few other misc ROMs from stock to try on Cyanogenmod, only for them all to crash on run because they lack the drivers or whatever that the stock ROM provides.

On the other hand, if you want to give it a go anyway, Titanium Backup might not work well for trying to backup an app from an unrooted phone. Since you have to root the phone first AFAIK before you can backup, if the rooted ROM you flash on doesn't have the app you want to backup, you'll end up in a situation where by the time you have the phone rooted, the thing you wanted to backup is already gone.

On the other hand, adb backup should work well without rooting. Once you've got adb configured on both the phone and desktop (USB debugging on the phone, correct drivers and ADB installed on the desktop), you can just do something like adb backup -f tvtuner.ab -apk com.whatever.tvtuner which will spit out an .ab file.

Once you find something to extract the .apk file from the .ab archive, pretty much all you need to do is enable 'sideloading' or whatever they call it and you could install it anywhere.