The GFCI outlet already protects the cord.

No. If the extension cord is plugged into a GFCI-protected outlet, the cord itself does not need an additional GFCI. The outlet handles that.

The only thing to watch is the cord’s condition and rating. A frayed or indoor-only cord used outdoors is still a bad idea, even with GFCI protection. GFCI prevents shock but doesn’t stop a fire from a damaged cord.

So plug away. Just make sure the cord is in good shape and suited for the environment. GFCI is there to protect you at the source, not to fix a broken extension cord.