"Don't take it personally, she's rude to everyone."
-Ron Weasley (DH8)
An aunt of Molly Weasley’s (DH4) who looks like a “bad-tempered flamingo,” Muriel is quite a character. She attends Bill and Fleur’s wedding, but talks loudly throughout it and doesn’t seem to have a filter, telling Hermione she has skinny ankles and George that his ears are lopsided (DH8). However, she offers her goblin-made tiara for Fleur to wear in the wedding (HBP29) and offers her house as a safe place for members of the Order of the Phoenix to hide from Death Eaters, even when that means the entire Weasley family moving in (DH5, DH24). Muriel is apparently is a memorable kisser (HBP14), and lives near the Burrow in Ottery St. Catchpole (DH5).
Surname possibly Prewett? As Molly's aunt, Muriel could be either the sister or the sister-in-law of Molly's parents. Even if Muriel is a connection through Molly's father, a Prewett, that doesn't necessarily mean that Muriel's adult surname was Prewett. The only thing that is certain is that Muriel is not a Weasley. (Many thanks to Yvonne B. who pointed this out.)
Muriel's blood status is uncertain, but it stands to reason that she is not a Muggle-born since the goblin-made tiara has been in her family for multiple generations (DH8).
Other canon notes and references
Muriel used to spend every Christmas with the Weasleys at the Burrow, but she stopped coming after Fred and George detonated a Dungbomb underneath her seat during Christmas dinner one year. She was apparently upset enough by this that Arthur Weasley suspects that the twins have since been excluded from the beneficiaries in Muriel's will. (DH8)
Muriel is a fan and loyal reader of Rita Skeeter (DH8).