The family name card that you print for the temple does not expire, even if the reservation on FamilySearch does. Old cards with barcodes (instead of QR codes) will still work as well.
If you've had a family name card for more than a few weeks, please check Family Tree to confirm that the ancestor still needs the ordinance performed. The ordinance could have been shared with the temple, or someone else may have reserved it.
If so, you may simply destroy the family name card. It is no longer needed.
Related articles
Where can I find the expiration date for my reserved ordinances?
What happens when ordinance reservations expire?
How do I view my ancestor's ordinances in Family Tree?