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