How to clean non-slip strips on bottom of my tub?

I would use a scrub brush and bar keepers friend.

What is your tub made of?

The adhesive is rather serious on those strips so you might want to try olive oil or lemon oil to remove it. You will have to get the top layer of the strips off first. Hopefully, you can loosen an edge and pull off to reveal the underside where it's glued down.

Have you tried Soft Scrub? You don't want to remove it, right?

Try Heavy Duty Mr. Clean Magic Eraser. If that doesn't get it clean, I think you will have to live with it!

I always used cleanser like Comet and a toothbrush. They are textured and the soap and dirt build up in the crevices. Try Awesome purchased in most dollar stores. Spray bottle of 16 oz. for $1 that cleans things that other cleaners will not touch. Spray one let it sit for about 30 seconds, go over lightly with tooth brush.