that's a nice strap, i'd leave it alone. i favor straps with suede bottoms (that grip the shoulder/shirt) like that with my basses - i like the fact that they help the bass to stay put when i'm playing.
i just use raw belt leather that i dye black, cut to size and poke holes in. straps get better (more supple) as they age, and they're cheap. and my basses stay put.

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