One initial point: you refer to "printed money", which would normally be restricted to currency in circulation (notes and coins); the parts of the money supply that are electronic are literally not printed.
Borrowing on a credit card creates a credit card receivable, which is not normally considered part of most money supply figures. However, if it were part of a securitisation, it might eventually show up as part of the wider money supply aggregates (M3). (The securitisation ends up funded by a money market fund, and money market funds are typically part of "wide" money supply definitions.)
Are we collectively shooting ourselves in the foot as a result of this fabricated money?
If you think the only objective policy is to preserve the value of the currency unit, perhaps. The relationship between money supply growth and inflation is debatable, but it is seems safe to say that extremely rapid borrowing by the non-financial sector is associated with higher inflation. However, if the objective is to enhance output and employment, not really.
Credit cards are just another form of credit. The growth of modern capitalist economies is associated with credit expansion. It may be possible to have a growing economy without credit growth, but it would be very difficult. Investment could only be funded by profits, and it would be difficult to offset the withdrawal of financial assets from circulation by the savings desires of households. Without credit, the only mechanism to recirculate savings to the business sector is via equity injections. In practice, direct equity investment is not a significant source of funding for the business sector. That is, stopping credit growth chokes off funding for businesses in practice.
In other words, we can say that society faces a trade-off between monetary stability and growth; the exact nature of that trade-off is somewhat fuzzy.