We don't have synonyms for minthe yet — it may be a rare, specialized, newly coined, or misspelled word. The closest thesaurus entries we have are mintie, inthe and menthe.
(n) :
(Greek mythology) A nymph (associated with Mount Minthe in southern Greece) with whom Hades had an affair before the taking of Persephone and she complained in jealousy that she is more nobler in form than Persephone(his wife) and when Demeter(her mother) heard of it, she trampled the nymph under her foot and turned the her into herb mint.
(n) :
(Greek mythology) A nymph (associated with Mount Minthe in southern Greece) with whom Hades had an affair before the taking of Persephone and she complained in jealousy that she is more nobler in form than Persephone(his wife) and when Demeter(her mother) heard of it, she trampled the nymph under her foot and turned the her into herb mint.