Pilgrim's rhymes with:
pilgrims, pilgrims, pilgrims, pilgrims, seagram's, seagrams, seagrams', abram's, abrams, angstroms, doldrums, eproms, forum's, forums, nordstrom's, nordstroms, nostrums, pilgrims, quorums, santorum's, seagram's, seagrams, seagrams', spectrum's, spectrums, tantrums, tungsrom's
Pilgrim's sounds like:
pilgrimage, pilgrimages, pilgrims, polygram's