what to do with my cat on my speaker grills

Spray bottle and a sisal covered scratching post nearby (that feels better than speaker grill covers)

I think I have the purrrrrrrrfect solution! Sorry I couldn't resist.
There are always a couple of kitty's in my house. My wife loves them and I must
admit I have grown quite fond of them myself.. I have never had a problem
with the cats bothering my speaker grills, but I must admit, I expect it could happen.
My solution is to make a second pair of grills and not worry about it.
This can't be done with all speakers, but some are very easy to retrofit.
I've done this twice with a pair of Spendors,
and with my current Silverline speakers.
It's not hard if you own a CNC router table, which I do, but can be accomplished with common tools and
some patience.
Both sets IMO actually came our better and
more aesthetically pleasing than the originals.
Speaker cloth, if you like black is readily available at a local fabric store.
My way of co existing.
Give the little fur balls a scratch under their ears for me.

Good luck

A skewer will do... insert in either end.

Good advice from Rhyno.

ditch the cat is the only sure fire way