I used to remove them too until I had a callback from doing it.
The lady called and said that the toilet that I re-built wasn't turning off.
So when I looked at it, and raised the float up with my finger to get it to shut off, it didn't. So upon removing the hood on top of the Fluidmaster fill valve, I saw a small piece of solder which was preventing the unit from completely turning off. She had copper water piping in the house and apparently a small piece of solder had traveled up into the fluidmaster. Had I not removed the little inlet screen in the shank of the ballcock, I would never have had a callback.
So now, I don't remove them. That will catch little pieces of trash and keep the trash out of the top of the unit.
It's funny you mention that because it's the same reason we do remove them. If the solder wasn't from you then it's not a "call back". You put in a new fill valve and it coincidentally got sediment soon there after. Had the screen been in it may have not filled fast enough or made a loud noise also resulting in a call back. I have had all of these things happen and I decided it's better to have the sediment appear at the top where you can easily clean it, and tell them it's not a call back, I can't control what's in their waterr, unless....
.....if there is a reason to worry about sediment I will address that by suggesting a whole house filter. If the house is plumbed with rusty/flaking galv I make sure to tell them they may have further issues. I will sometimes suggest they let me install a wye strainer before the stop.
if you leave the screen in and it gets sediment you still have a "callback" and they may ask why you didn't purge the line before hooking up the new fill valve. Except with the screen in now it's a 5min job of disconnecting the supply line with a towel and bucket underneath and trying to pull out the sediment and the screen to clean it. Then you put it all back together and hope more doesn't show up.
With no screen you just shut the stop, take the top off the fill valve, cup your hand over it, run the water for 30secs, and put the top back on. Takes less than a minute and you flushed the line at a rate faster than the fill valve will normally draw, so it should have cleared all the loose sediment. Also, if the sediment damages the fill valve you can just replace the top portion leaving the shank/supply line alone.
I understand why you would keep the screen in, my guess is your customers mostly have city water and no galv lines. We have a lot more sediment issues to deal with because of wells and old galv. Taking the screen out has worked better for us.