Delivered via Amazon, it's TRQ brand in a TRQ labeled box. Is it cool that the end cap was loose and a 1/2 cup or so of grease was inside the bag? Can I just tap the cap back in place with a rubber mallet and GTG? Does this piece need to be pressed in with a machine?

Unless there was a hell of a lot more padding in that box, "normal" (i.e. rough) handling would be enough to dislodge that cap.

Edit: also with extreme temps, and nothing to hold it in, pressure buildup might have popped it off. That would explain grease everywhere.

You can just tap them in. As long as it’s a snug fit, that’s all they’re meant to do. Wipe the grease off and send it.