SOME POSSIBLE OPTIONS:
If your PUP has an outdoor shower, it is likely that it is located somewhat lower than the sink faucet. If so:
1) turn off the pump;
2) open the kitchen sink faucet;
3) go to the outdoor shower and open the valves keeping the shower head near the ground.
4) TURN OFF THE SHOWER VALVES.
5) TURN OFF THE SINK VALVES.
This should drain the water in the faucet.
My PUP has winterizing drain valves under the sink...at the low point in the plumbing. These are t-shaped handles that you pull, and they drain water thru pex through the floor and onto the ground. Your camper may have similar. If so, turn off the pump, open the sink valves and pull these drains. Allow the water to drain out of the lines, THEN CLOSE THEM. CLOSE THE SINK VALVES.
(Closing the valves prevents the obvious mess when you turn on the pump next time and create a flood and/or dump some of your precious water in the holding tank.
Your camper may not have either of these options. When I had a PUP similar to yours, we simply put an old towel on the floor to absorb water AND to protect the floor from the support leg. In Colorado, where humidity is very low, we didn't have to worry about moisture in the towel. It would dry quickly. But in humid climates, allow the towel to absorb the sink water, then replace the towel with a throw rug to protect the floor from the support leg.