I saw that too. I wondered how only the patch survived, but not the rest of the suit.
Then it hit me. The patch probably was never on a suit. I'll bet they take a whole box of mission patches up with them. After the trip they can use them as gifts, or sell them in the giftshop (or whatever) as mission patches "that have actually been in space". Seems reasonable to me. There might be hundreds of them.
They would survive because they flutter almost immediately to a slow speed and don't get hot.
You are correct.
They take mission patches, small US flags (and probably Israeli flags for this mission) and other stuff. They use them as gifts or incentive awards for NASA and contractor workers or schools or govt. officials etc.