My Island Gypsy 36 had a grey water sump like that, collecting from shower, washbasin and galley sink.The "flipper' switch used to gum up. It had no strainer, yours looks like an added afterthought. Mine had a 2000gpm bilge pump similarly actuated, tested while removed from the sump it fired an impressive jet of water several meters.
You can buy an "in-line" strainer for the input hose leading into the Sump (if you cannot find a replacement). I had an in-line strainer on my last boat that you could simply unscrew and clean out. You didn't have to take the hose clamps off to service the stainer. Just a thought...... Many types out there to choose from..... https://www.amazon.com/Female-Strai...pcontext&ref_=fplfs&psc=1&smid=A2299WSW78KSX9
It looks like a DIY kitchen strainer used to keep hair, etc., out of the pump. If it were my project, I'd switch to polyester batting. It may require a sewing machine to make a polyester batting "sock" to fit over the inlet. The only difficulty would be to ensure that the filter sock not lay on top of the float switch. Maybe the old strainer (or a new one) could be placed over the float switch. My main reason for using a polyester sock in my sump is that it can be replaced by simply tossing it in the garbage and attaching a new one, similar to a bag in a vacuum cleaner. Polyester batting is cheap at any fabric store.
What might be really simple for you to try is to attach a 2'x2' piece of polyester batting to the edges of the sump (using binder clips) so that it sags under the water inlet. Don't let it bag so much that it interferes with the float switch. No sewing required and you simply look in to the sump to see if it needs replacing. It will catch hair and soap scum better than the stainless strainer (and no cleaning out a strainer).