Refitting rhymes with:
befitting, fitting, acquitting, admitting, befitting, bitting, committing, emitting, fitting, flitting, gritting, hitting, knitting, omitting, permitting, pitting, quitting, resubmitting, sitting, slitting, spitting, splitting, submitting, transmitting, unremitting, unwitting, whitting, witting
Refitting sounds like:
rafting, rebutting, refuting, repeating, repetitions, repudiating, reputations, riveting