He said my tools would be given back to me once I get back to the town... but I have nothing! not in the drop-off box, not in the the mail... it's just gone
There are two probable answers, along with some questions.
Have you checked your inventory? If not, do so.All your items should still be there. Next, if you don't know, the Gyroid at the island does not give the tools to you. They are only to borrow.This should explain why putting the rental tools into the drop-off box is impossible.
In conclusion, you probably misread the animal's statement.(but, you never really told us who you were speaking with..)