Hello,
I made the mistake of looking at the profile for George Villiers, Duke of Bucks and noticed he has some rogue relatives.
Sir Thomas Compton who married Mary Beaumont (Countess of Buckingham) had no heir, and he was definitely not the vicar of Sutton Valance.
From a two minute mooch on the internet you can find that the children on this tree are mentioned in the will of Thomas Compton, the real vicar of Sutton Valance ; and this Thomas Compton (not a knight) died in April 1606 - (which would have made it a bit awkward for him to marry Mary Beaumont.)
e.g. https://www.ancestry.com/boards/localities.britisles.england.ken.ge...
From 'The History and Topographical Survey of the County of Kent: Volume 2' - found at https://www.british-history.ac.uk/survey-kent/vol2/pp227-263
re: the Comptons & the parish of Erith.
'...Henry, lord Compton, above-mentioned, settled the manor of Eyrth on Sir Thomas Compton, his second son by his first lady, on his marriage with Mary, countess of Buckingham, relict of Sir George Villars, and mother of George, duke of Buckingham. He died without issue, and devised it by his will to his great nephew, Sir William Compton, third son of Spencer, earl of Northampton, only son of William, lord Compton, who was created earl of Northampton, by king James I. in the 16th year of his reign, and was elder brother to Sir Thomas Compton, possessor of this manor, as before-mentioned. (fn. 28) Sir William Compton was a most loyal and valiant gentleman, and engaged in the civil wars for king Charles I. in the 18th year of his age, during which he was made governor of Banbury-castle, and in 1648 major-general of his Majesty's forces. Soon after which he conveyed the manor of Eryth to Mr. Lodowick, of London; who quickly sold it to Nicholas Vanacker, esq. merchant of that city...'