Either pack it in a hard case and then in a plain cardboard box just so it doesn't look too much like a firearm (like the size isn't a giveaway!) or wrap it good and put it in the cardboard box without the hard case. Your choice to save a couple of dollars shipping, and the possibility of the manufacturer losing the hard case.
You do not need an FFL to ship a firearm to a manufacture for repair, and they can ship it directly back to you, since it already has gone through the 4473 previously.
I have had to ship a couple hand guns back to Ruger. I made sure I had a reference number from them in writing along with the exact shipping address. I made sure the guns were unloaded. Packed it in a plain brown box with a letter inside with the reference number they provided and a brief explanation of why it was shipped to them.
I decided to ship it over night with a tracking number and signature confirmation required. I also opted to for the insurance. I then put it in the mail to them. Once I saw the confirmation and signature I also touched base with them again just confirm it arrived. It should be a simple process but, I do recommend keeping detailed notes for your records and traceability. Once it comes back to you just double check the serial number.