Thanks for all the replies, everyone! I figured rinsing it and letting it dry would be fine. I'm going to start putting them in an airtight container, too. I had wrapped the current one in a paper towel after rinsing and then put it in the fridge. I was surprised to hear from the lady I bought these from (I asked her about it on facebook) and she said to not put them in the fridge and just wrap them in a paper towel and they'd be fine.
I guess I feel better rinsing them since we have 3 cats and noticed some cat hair on the end she chewed. I guess I didn't vaccuum as well as I thought!
Thanks again for the advice. I'm going to continue to rinse and refrigerate them after hearing that it seems to be ok. I trust you all on here more than I do the lady at the store
. I just hesitate to leave it out with the cats in case they think they can carry it off and do who knows what to it!
So I think rinsing and refrigerating or freezing is the best option.