I tried using the Recruit Calling card and in doing so, when I went to resummoning my companion she came back with all her equipment, but her inventory was gone, all my materials she was holding were gone and she didn't drop a box anywhere for me to retrieve them.
I was able to locate the box that is spawned when you get the calling card, it had spawned in the roof of my building on top of a ceiling floor I had set up.