Even though Anthony and Nick are unfriendly rivals for Grace's affections (though Grace doesn't view Anthony as anything more than a friend), it seems unlikely that Anthony would just allow himself to enter Nick's house uninvited and not announce himself.
Nick and Sam come from New York (City, presumably), where locking doors is second-nature. Nick leaves his door unlocked, whereby Anthony allows himself entry into Nick's house and catches Nick and Grace at a sensitive moment.