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Hi, Linda. The earliest mention of anyone by either of these last names (and I checked Griggs, Greggs, Grymes, Grimes, etc.) is in 1790, when William Grimes posted security for someone else's wedding; then in January 1799 when Nicholas Grymes provided security for a marriage between Sylvester Grimes [last names appeared that way] married Sarah Davies.
There are no Greggs/ Griggs at all. There are several other Grimes/Grymes: Charlotte, Daniel, Emily, George, Henry, Sarah, Susan, Sylvester, William.
If any of these names rings a bell, let me know and I'll follow up.