Katherine Keats-Rohan in her Domesday People books, has this family indexed under 'de Gand' but refers to them also as 'de Gant'.
The Complete Peerage, 2nd ed., Vol. 7, refers to Gilbert, Earl of Lincoln as 'de Gant or Gaunt', but to his daughter Alice as de Gant only.
A charter issued by Alice used de Gant for herself and her father. https://babel.hathitrust.org/cgi/pt?id=njp.32101013255607;view=1up;seq=528 (not sure if this link will take you to the right page, but its Charter 1217, on page 492)
It would seem that at least some of the early sources are using de Gant and not 'm not sure where de Gaunt for this family comes from? Is it used because the later John of Gaunt, Duke of Lancaster was born in Ghent/Gaunt?