Normally one doesn't need to clean one's strop, but in this case for a second hand strop I'd wipe it down with a slightly damp cloth. I'd also try and clean the fabric a little as it looks quite dirty. I have a daily use Dovo strop that hangs in the bathroom on the towel rail. My wife uses hair spray so it became covered in the hair spray junk. I actually washed it (horrific, I know) but it came out fine.