The ancestry of Robert Montgomery cannot be identified from the Scottish charters in which his name is noticed. In view of this, I believe that his profile should be disconnected from the family of Arnulf, Earl of Pembroke, and his son Philip Montgomery.
In his 1906 account of the earls of Eglinton, the Reverend John Anderson reviewed the evidence, or the lack of it, for the ancestry of Robert of Montgomery. According to him, it had previously been claimed that Arnulf, Earl of Shrewsbury, was the father of: “the first Montgomerie who appears in Scotland, and this view is given effect to by the late Sir William Fraser in his Memorials of the Montgomeries, Earls of Eglinton. But the reasons advance by him are very unsubstantial and without the sanction of any valid evidence, while on the other hand, though the wife of Arnulf is known, there is no proof that he had any family”.
Source: The Scots Peerage etc. By Sir James Balfour Paul. Volume III (David Douglas, Edinburgh, 1906), pp. 421-2
Sixty-seven years or so later, writing in his account of the earliest Stewarts and their lands, the late G. W. S. Barrow had this to say about the Scottish family: “Montgomery in Wales had been given this name by the Norman earls of Shrewsbury before 1086. At any time thereafter, a person born at Montgomery or having his origins in the Castellany or the Honour of Montgomery (then included in Shropshire) might well have been given the surname ‘de Montgomery’. It is most unlikely that the Scottish family of Montgomery were related to the family which held the earldom of Shrewsbury until 1102, who took their name from Montgomery in Calvados. The Scottish Montgomerys probably came from the Castellany or Honour of Montgomery, which was close to the fief held in Shropshire by the FitzAlans.”
Source: The Kingdom of the Scots. Government, Church and Society from the eleventh to the fourteenth century. By G. W. S. Barrow (Edward Arnold, London, 1973), p. 344