Keats-Rohan, in the DD entries for Turold p. 1137 and for Turold's dau. Lucy p. 247, says Turold's wife was a dau. of William Malet.  This is repeated in the DP entry, p. 142, where ths Malet daughter has a sister who probably married Alfred of Lincoln.

While his daughter was indeed his heir, it is clear that he died enough before the onset of heraldry that no-one even invented any arms for him after his death.  So his arms cannot be quartered, as he does not have such.