FedEx delivery to wrong address?

I ordered a gift card online, to be delivered to me by FedEx. The package delivery required a signature. Yesterday I was not home when they attempted to deliver it, and they left a slip on my door that I signed to authorize them to leave the package at my door. Today I received an email that the package was delivered, and their package tracking said the same thing, but the package was not here and the slip I signed was still on my door. I called FedEx and was told that their package tracing indicated that it was mistakenly delivered to a completely different address and someone signed for it. They said they would contact the driver to get it straightened out, and that they'd call me back, but it's been 7 hours and I've heard nothing. So now some stranger has my gift card, and is probably enjoying a really nice free meal, thanks to FedEx. Is there anything I can do about this? Should FedEx reimburse me for the gift card? Am I just out of luck? How do I handle this?

Thanks in advance for your help!