Possible solutions
1: You can get a screw in plug designed to protect the city water inlet from Dust and debris when not hooked up, in fact you should already have one collared to it.. These actually work.
2: Some suggest this will not work, others it will
Remove the screen washer from the inlet, You will see a plastic "Button" NOTE.. YOU WILL GET WET
With pump on press, and release, the button
Sometimes "Crud" gets into the valve and doing this will flush it out
others say it will dislodge the seal and it will never work right.. But it's not working right now, and thus you should not do that. BUT.. It's already not sealing, so if you damage the seal, you have done no additional harm.