They've got a baseline of what you usually smell like. They get close to you in an intimate way. For everyone else it doesn't matter.
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I generally stick to shops that have showers, so am at least clean. When I get changed, which I always do when I get gome, I grab my own towel and just rub it all over myself. Unless the towels have been changed, or your bathroom dries the towels super well, there will be your own residual smell on the towel with a little bit of moisture. After doing this I can’t smell anything different.