Yeah, some of the IBM Selectrics and Brother typewriters back in the Eighties and Nineties had single use tapes that left a visible imprint.
And then there's the Dymo Label-it from the late Sixties:
en.wikipedia.org
It would generate an embossed plastic tape that had a peel-off back that had the imprint of whatever was printed on the label.
As long as you're not printing credit card numbers or personal identification numbers (like passport numbers, drivers license numbers, etc.), I fail to see a big risk.
The bigger risk was the deprecated carbon copy credit card imprint slips used with the old "knuckle buster" devices. These were phased out around the turn of the millenium, around the same time that stores started to move away from printing the full credit card number on charge receipts. Same thing with mailed statements; the full number is no longer on most correspondence.
This was around the same time that banks using social security numbers as account numbers discontinued this practice.
The relative risk of these used P-Touch label cartridges compared to so much online activity (including connecting to public wifi networks) is miniscule.
You can worry about it if you want but likely there are a thousand other things in your life that are a greater privacy/security risk (like weak passwords).