Mints get tricky if you are reading the Tortoise Table database, where is we encourage new owners to start.
Many mints are fine but orange mint is a species of “mentha piperata,” which the Tortoise Table lists as a do not feed: http://www.thetortoisetable.org.uk/plant-database/viewplants/?plant=512&c=5#.WmpjQCSIbmo. Other mints in this species are pennyroyal and peppermint; if you have ever sniffed or tasted those mints, you might have noticed they are particularly strong. If you have ever tasted an Altoids mint, it’s largely flavored with peppermint.
Anyway, this mint species contains something that *could* be hurtful if consumed in large quantities. That doesn’t mean it absolutely is bad, but we aren’t sure. As a new owner, however, you’ll probably feel better if you don’t let your tortoise near it.
I can’t imagine a tortoise eating much of it for any reason; given how strong it tastes.
I have offered my tort small amounts of apple mint and spearmint and he does not like it. My sulcata is NOT picky but there are a few things that he just does not like and mint is one of them.
I will sometimes put some crushed mint leaves in his enclosure if he poops in it to help with the smell.(I clean the poop out immediately but the smell can linger)