Reinfrid is not confirmed as a Taillebois, nor is it known whether he had any family before taking to religion.

"A certain Reinfrid, who had been a most valiant soldier of William the Conqueror, moved by sorrow at the wasted holy places at Whitby and elsewhere in the north, entered the monastery of Evesham with the intention of becoming a monk capable of repairing some of the mischief. After some time spent there, he returned to the north and journeyed to Streoneshalch, otherwise called Prestebi and Hwitebi. (fn. 3) He approached William de Percy, from whom he received the ruined monastery of St. Peter, with 2 carucates of land, and there he set to work to resuscitate the monastic life. He was joined by many, including Serlo de Percy, the founder's brother, and numerous other gifts were made to the revived house, which followed the Benedictine rule. From the description of the old monastery when it was given to Reinfrid it comprised about forty roofless and ruined monasteria vel oratoria, (fn. 4) which calls to mind some of the Irish monastic ruins at the present day with their numerous chapels and cells.

"The original gift of William de Percy (fn. 5) included the monastery of St. Peter at Whitby (or Streoneshalch), the town and port of Whitby, the parish church of St. Mary there, and its six dependent chapels of Filing, Hawsker, Sneaton, Ugglebarnby, Dunsley, and Aislaby (to follow the modern spelling), five mills (including that of Ruswarp, still existing), the town of Hackness with its two mills, and the parish church of St. Mary there, and the church of St. Peter at Hackness ' where our monks served God, died, and were buried,' and various other gifts enumerated in the ' Memorial' in the abbot's book. The latter authority relates that Prior Reinfrid, having ruled the monastery many years, was accidentally killed at Ormesbridge by a piece of timber falling upon him, and that he was buried, in the cemetery of St. Peter at Hackness, when he was succeeded by Serlo de Percy as prior. (fn. 6) " https://www.british-history.ac.uk/vch/yorks/vol3/pp101-105

From http://newsgroups.derkeiler.com/Archive/Soc/soc.genealogy.medieval/...

According to what I have found Ivo Taillebois's father was Reinfrid and his father was Reinfrid.

Reinfrid was listed as a soldier and as the 1st prior of Whitby Abbey and buried at Hackness, Yorkshire.

Ivo was at the seige of Ely in 1071. Sheriff of co. Lancaster 1086, had custody of the See of Durham after the expulsion of the bishop for taking sides with Duke Robert. He was Dapifer in 1091 at which time the king gave him the Lordship of Kendal and his family is Angevin. Davis, Regesta, no.'s 408,409 Ivo was made a Marcher Baron under William Rufus and was"enfeoffed... of the whole of Ewecross wapentake,then later the Lordship of Burton-in-Lonsdale, Later the Barony of Kendal with the southwest portion of Cumberland described as the Barony of Copeland" by J.C. Holye, Oxford:Clarendon,1961. Chart compiled by Alfred Ramsford p.38 Nov. 1932.

Sources

https://gw.geneanet.org/belfast8?lang=en&p=rolf+reinfried+de&n=tail...

https://www.genealogieonline.nl/en/genealogie-benjamins-poppes/I213...