Peggie Hall will no doubt weigh in on this and do whatever she says.
What causes you to believe the holding tank is full?
If the symptom is fluids running back into the toilet bowl after flushing, there are several common causes.
In no particular order.
1) the vent line for the holding tank is plugged. When you pump the toilet it pressurizes the holding tank and that pressure forces the effluent back into the bowl.
2) the joker valve is shot. This is a one way valve that allows stuff to flow out of the toilet and into the lines to the holding tank. If the boat is new to you, this is a likely culprit. Even it if is not the cause, replacing it every year or two (depending on use) is a good idea.
3) the water intake line is siphoning seawater back into the bowl. Is there a vented loop between the pump and the bowl? To see if this is an issue, close the seacock after flushing. If the bowl fills, then the problem is elsewhere.
While we're waiting for Peggie to weigh in, pick up a copy of her book,
The New Get Rid of Boat Odors: A Boat Owner’s Guide to Marine Sanitation Systems and Other Sources of Aggravation and Odor it is a worthwhile investment.