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The bits could also be knocked loose on the other pass and picked up on the return.

With the heel of your hand, work out the scratches so you can't see them as much. Then do one pass each way...

Very carefully check and see if there is a frown on edge by holding it edge down VERY lightly on a known flat object and hold it up to a light, there shouldn't be any spots where light comes through...

As others have said please post pictures.
Are the scratches happening in both directions when you strop or just one?

The only razors that left scratches for me were a spike point razor and I...