There is a check valve in the water pump that is supposed to prevent city water from flowing to the fresh water holding tank. There could be a particle of sediment preventing the valve from seating correctly. Or the valve could have just failed.
You might try removing the city water and allow the pump to run water from the fresh water tank in an attempt to flush any sediment from the valve. If that does not help you can purchase a check valve that you can connect to the pump. That would be considerably cheaper than replacing the pump.
If you don't already, always use a filter when filling the fresh water tank. It will reduce the chance of sediment creating problems with the valves in the camper.
Hope this helps.
Chuck - Sparta, TN
2012 Jay Flight 22FB, 2 x Honda EU2000i
2013 GMC Yukon XL Denali AWD
EDUCATION is what you get when you read the fine print.....
EXPERIENCE is what you get when you don't.