Hi Jamie.
In the Grimston pedigree the tinctures of the Lion differ (Gules vs. Sable) to those depicted in quarter 714.
With quarter 717, the blazon 'Gules on a Bend Argent three Mullets Sable' is attributed to the following surnames ...
BRABAZON, DELAVALL, DISHINGTON(Scotland), LIDDELL(Scotland), OVINGTON, RERESBY, RESBYE(Suffolk), ROSBY(Yorkshire). This info comes from Papworth's Ordinary along with cross-references to Burke's General Armory. There are no references to those surnames in the Supplement to Burke's GA or in General Armory II. So, perhaps two different families with close surnames?
Quarter 718 is indeed the arms of RISBYE of County Suffolk. (Burkes GA)
I would suggest that the College o Arms might be the only place where you could verify the facts.