John
Unless your grandfather was posh, it is more likely that he was a member of Earlsferry Thistle Golf Club, an artisan's club started in 1875 and of which Braid was a member. Try giving them a call at +1333-330301.
Those were heady times for Elie, as in addition to Braid (and your Granda!), Braid's uncle, Douglas Rolland, as well as the Simpson brothers (Archie, Bob and Jack) were all playing out of there. All were among the very top players of that age, with Jack Simpson winning the 1884 Open and Rolland and Archie Simpson finishing as Open runner up on at least two occasions each in . Rolland also had a hand in the original design at Rye, and Archie Simpson was a highly gifted designer, with Murcar and much of Royal Aberdeen to his credit. He worked with Old Tom Morris at Both Cruden Bay and Dornoch.
Archie should also be of interest to you in that he left Scotland in 1911 to become the first professional at the Country Club of Detroit. He stayed there until 1920-21 and might possibly have had contact with your grandfather. I've tried to get some information on Archie's tenure there from CCofD, but I seem to have more information than they do, and/or they don't want to share with me what they have.
Archie also died in Detroit in the 1950's (1955) at age 88.
Hope this helps. If you have any luck with Earlsferry Thistle and need some liaison, let me know. I live 40 minutes away from them.
Rich