It is best to do double-duty with screens in the valve itself, and
backup at the faucet end of the hoses with hose screens as mentioned
elsewhere in this thread. You can purchase replacement screens for the
fill valve at an appliance parts store, then install them with a long
socket, such as 1/2" size. Sometimes it is a bit difficult to get the
screen seated correctly. You may have to use gentle pressure from a
small screwdriver to press in one side if it starts going cockeyed.
Or, just replace the whole valve if you can get to it (should be about
$30, not $100 for the part).
By the way, for everyone else, even if you don't have problems with
your valve, it is best to install hose screens. Everyone should have
them. This the best insurance against overflow due to debris in the
valve. New washing machines rarely come with hose screens for the
hoses, but replacement hoses sometimes do.