Printed seed phrases aren't meant to be shared, and even if someone would get their hands on it, they wouldn't be interested to know which printer you used. They would just take your money.
I suppose a very theoretical risk would be an attacker finding your seed phrase and then tracking you down via this tracking information to extort you for other seed phrases, other wallets, passphrases, etc.
Just another minor point to add to the list of "Why over complicate things with a printer?". Write your seed phrase down, laminate the paper if you so choose, job done.