antmire

Alteration of pismire by the Puritan settlers of the New World, equivalent to ant +‎ mire (“ant”, obsolete). The Puritans were known to have adopted new terms or to have modified other ones to have less potential for offensiveness, hence the use of rooster for cock in North America, chickadee for tit, etc.

The form anty-mire is likely a minced alteration of pissymire, a variant of pismire.