I am surprised to read this. What kind of systems are these? How are they able to monitor if a private key is leaked or not.
They will trawl forums like this one, Reddit, Twitter, etc., on the hunt for private keys which have been shared. Then they import those private keys in to their software, which generates the corresponding addresses and watches them for any incoming transactions.
Other sources of private keys they could import include hacked cloud storage, hacked password manager databases, hacked email accounts, brain wallets, and so on.
& how does it recognize the gibberish code as pvt key anyways?
Simply search for any 51 character string beginning with "5", or 52 character string beginning with "K" or "L".