Archetypal authoritarian teacher personality, Miss Finster has a strong desire for a school in which children are not allowed to have fun or act like children. She is feared by all the children, and is always closely followed by her teacher's pet, the equally nefarious Randall J. Weems, who is also largely disliked by the other students. Her disposition plays an important part in maintaining stability within the society of the playground providing a common enemy for the children of Third Street.
As shown in The Story if the Whomps, she also shows a sense of sadism by treating make-up words kids think of as swear words and sends them to Prickly's office for a punishment they rightfully don't deserve..
Despite her authoritarian nature, she has been shown to be a deeper and kinder person at times. Outside school, she has shown to be friendly, fun and supportive of others as shown with several interactions with the gang outside of school.
Despite her age, Finster is an accomplished fighter and is generally in excellent physical condition, demonstrated on a number of occasions. Former Navy commodore from 1952 to 1954 (Korean War.) Her surname "Finster" is the German word for "sinister".
In her youth, she had red hair and wore large blue glasses. In her senior years, her hair is short and gray and she now wears triangular glasses. Her traditional wear is a yellow dress with a diamond pattern.
In the feature film Recess: School's Out, it is revealed that Ms. Finster has been holding back on the school's ice cream supply and intends to sell it back to the district in exchange for chalk and erasers. When Randall briefs her about the kids' last day of school activities, as well as TJ and his friends' absence, she takes no notice and for that her plans are derailed when TJ and his friends catapult the ice cream down on the students. She is then seen with Miss Grotke and Principle Prickly watching the kids leave when the school day ends.
A few days later, Ms. Finster is boxing a punch bag when she hears the doorbell, thinking it is the pizza delivery, but it turns out to be Randall. He informs her about TJ and his friends breaking in to the school (in reality they were trying to rescue a captive Principle Prickly) and she takes action to have the kids tried. Once there, Ms. Finster and Randall make two unsuccessful attempts to get into the school since the doors are locked (and electrified): First, she climbs up the rope to the window left by Mikey Blumberg and it snaps under her weight. Then she tries going backwards through the basement window, only to get stuck in the window frame ("Curse these bodacious hips of mine!" she adds). While Randall goes back to her house for some butter to loosen her up, Ms. Finster witnesses the tractor beam displaying it's laser ray at the moon and she gets even more suspicious when she sees the gang (minus a captured TJ) being chased by two ninjas.
In Principle Prickly's flashback of 1968, it has been shown that Muriel had been in a relationship with Phillium Benedict but it quickly ended when she realized that she could never be in love with a corrupt individual. In the present, after failing to convince two policemen, Ms. Finster rounds up the staff to take back the school with the additional help of the students.
Phillium sees her and is amazed that she is still gorgeous as before. She ignores his flattery by calling him a "two-bit recess hating pretty boy". He pleads with her to take him back but she angrily refuses and fights off his men. She saves T.J. from Kojak by beating the man up and telling the grateful T.J., she's just doing her job.
In the end, she offers Ms. Grotke a boxing vs. karate match, but Ms. Grotke is unsure since she only uses her martial arts for self defense purposes only.
When Miss Finster and the recess gang go to Kauai she goes to the spa.
In terms of inter-personal relationships, Miss Finster has been shown to have a crush on the school's janitor, Hank and is friends with Spinelli's parents. There are even moments where Miss Finster gives advice to Spinelli when she is in trouble. Of particular note is that she used to have a much sunnier disposition and throughout the series glimpses of this are seen with occasional references to her experiences in Guam.
She did at one point in the late sixties have a relationship with Phillium Benedict, but broke up with him after he tried to cancel recess. Even when they meet up again, she expresses her disdain towards him, which was warrented after everything he recently did.
Miss Finster seems to become nicer as the series progressed.