Leaking check valve in that line

Most people have that problem most of the time. I fill my tanks
completely full with water and add cleaner and let set for a few days
to clean, but you waited until you are ready to go, so I guess you
watch & empty often.

The "check valve" is defective and stuck open on your City Water inlet line.

If you pull-off the debris screen inside the City Water connector that
"filters" the water that passes through this inlet, you will find a little
"button".  If you depress and release this button several times, you may get
it to reseat - blocking the back-flow of water from the pump.  You may wish to
have an assistant help with their hand on the pump switch to turn the pump
on-and-off a couple of times while you are outside manipulating the check
valve button, trying to get it to reseat.

The permanent solution for the repeated troubles *I* had with the flaky
back-flow-preventing check valve on my rig was to simply install a common
valve in the City Water line just inside the coach (inside a cabinet in my
case).  Since I use city water (as opposed to the demand pump) only once per
year, the new valve is normally closed except for that one time per year AND
when I winterize the system.  Then, with the water pump ON, I open the (new)
valve briefly to force antifreeze solution back out through the City Water
inlet.

This is a common problem.  Debris (cooking fat and other crud) foul the probe
contacts thereby giving the false indicator reading.

Thoroughly cleaning the gray water tank MAY fix the problem.  The fix
suggested by the OP is a good one, when you have the time.   Good luck.