Transfer pump works okay with 5/8 garden hose. Occasionally a pebble will get suck into the pump and damage the impeller. I tried one time to put the hose strainer between the end of the hose and the pump inflow port. But it wouldn't pump.
But what if I put the strainer further down the hose. Maybe add a section of hose and the necessary fitting. Do you think it will filter out pebbles?

That screen is just too restrictive. I would suggest something like this (see image). With something like this, you can see when the filtered area needs cleaning, and it prevents damage to the pump, while not restricting the pump so much. You will need some fittings to make it hook to garden hose, but that should be simple.

Thanks that is wonderful information. I wonder what they call that part. It look great.

Google "water transfer pump filter" then click on images and there are all kinds of options. Im sure you can find something to meet your needs here. What exactly are you using the pump for?

A small pond. Send pictures to Grainger Supplies to see if they have a part like that.
I'v been told they have a similar strainer, but you have to cut the garden hose connections off.
Because it twist into the hose rather than screw on, and then it is held on by a pipe clamp.
Sorry I have to chop up my garden hose.

Let me know how things work out.