Ditto the water. Plus a bit of time.
Assuming it is paper intended for toilets, a good dose of water with a couple of days to soak should decompose things enough to clear the tank.
As Doc noted, don't drain the tank until it is at least half full. So add water to get it at least half full, wait a couple of days, then dump and you should have a reasonably clear tank.
If you have stationary or other stuff in the tank that isn't intended for the sewer, then you'll need to fish it out.
I think some folks get overly concerned about RV toilet paper. There really aren't many brands or types of toilet paper sold these days that won't decompose rather rapidly (there's even an add with some bears talking about the problem of tp that decomposed rapidly enough to leave bits).
The key is to make sure you keep enough water in your black tank when in use to cover any solids. Water conservation is great but there is a point where it goes too far. Water serves many purposes in the black tank.