I'm sorry. Perhaps this will help...
Do NOT purchase more horsehide. If you already have a good HA horsehide strop, why not just clean it up? Put the diamond stuff on cowhide (if you like the feel of leather,) or on a piece of MDF.
Give the horsie a bath, first with waterless hand cleaner (done two or three times to be sure to get out all the residue,) and a quick wipe with some lighter fluid to REALLY get out all the residue, then a light rub with some leather conditioner such as Lexol. If you don't have any of that, any good quality shoe cream (NOT WAX SHOE POLISH!!!!) stuff that will be absorbed into the leather to rehydrate it will make it as good as new. If you plan to skip the shoe cream, skip the lighter fluid and give an extra cleaning with the waterless hand cleaner. Just be sure that there is no pumice in the hand cleaner or it will scratch the leather. That won't ruin its effect, only its looks.
Stitchawl