Her phone would not need to have gone missing for one of her housemates to have lifted the card and used it in a restaurant app to place the orders, then put the card back later.
I agree with Valley Girl that you'll likely have to honor the claim without any evidence from the restaurants that she was not the one making the food orders. And I also agree that you should see whether the timing of the purchases is such that you will be able to impose some second-tier liability on her for not notifying you of the missing card within 2 days of realizing she didn't have it.
John S. Burnett
Fighting for Compliance since 1976
Bankers' Threads User #8