Welcome to the oops club.
I have only used one side of my strops so far as I am still occasionally getting a little cut from an accidental downward stroke or more often letting the strop run off the end of the knife and having the tip dig into the leather.
However for my needs so far the cut strop, while a little bumpy, still does a good enough job.
Marc thanks for the reminder that replacement leather is available so inexpensively. I plan on ordering the 1500/glass stone/platen set and will make sure I get a few replacements pieces.
Bob