Rose is a side character who has yet to make on on camera experience. She was Jessie's grandmother. The first mention of Rose occured in the video "Rose." which described her funeral and her death, possibly from an attack by the Rake. This was further fleshed out in The Rose Article where it was revealed that he husband's name was William.
There is also a mention of a "William" and a "Rose" in the original Rake creepypasta further connecting them to both Linnie and The Rake. Whether Jessie's grandparents and the characters mentioned in the creepypasta are the same is unknown.
Dr. James Corenthal mentions a Rose and William in two of his journal entries from 1990. He mentions them as people he seems to know well, but not the exact relation to him. He mentions they live in rural Pennslyvania (Not too far from Lambertville).