BE1883 (Booth Delamere of Dunham Massie & Warrington) identifies Sir Thomas's wife as a dau of Sir George Carrington, widow of _ Weever. Maddison identifies her as Isabell, dau of Sir William Carrington of Carrington, widow of _ Wever.
The dates suggest that Anne was 2nd wife of the John of this generation.
Gilbert is not mentioned by Maddison in his pedigree on the Booths of Killingholme but he is described in his pedigree on the Booths of Goxhill as "2nd son of .... Booth of Barton, was the first that came into Lincolnshire".