Disconnect or turn off the city water supply. Turn on the pump, and let it pump a gallon or so of water out of the tank. Start-stop the flow a few times. Be snappy about it, not gentle. If there is a bit of grit in the anti-backflow device, this may flush it out.
If no help: Find the make (almost certainly ShurFlo) and Model of the pump. Then go to the mfr's web site and look up the pump. It will tell you if the pump has an integral anti-backflow device. Most do. If it does not have one, you need to look for the problem elsewhere. If it does, then you need to consider repair or replace. SurFlo has a repair kit for the pump head on many of its pumps. This is where the anti-backflow device would be located. Not expensive, and easy installation.
Bill