Stepping in here as a 4th and 5th grade teacher.
Yes, there are some behavioral components that I attach to grades. For example, if students are required to make some type of presentation to their classmates, one part of their grade (maybe about 10-20% of the final project grade) is based on what I call "listening to others" -- when it's time for OTHER kids to present, are they being attentive and respectful? So, a student could have a wonderful presentation with all of the necessary components...and get an A- (or whatever) because he/she failed to be respectful when his/her classmates were presenting their projects. I also have a grade penalty attached to assignments that are turned in late (which is a "behavior" issue) -- if you have every point correct but you turn it in a day late, you get a 90% instead of a 100%. So, yes, everything that happens within my classroom is "fair game" in my opinion in terms of having a grade assigned to it. One thing to remember is that teachers are pretty limited in terms of what we can use to penalize students -- I can mess with grades or I can mess with recess time (and teachers in some schools can't do THAT). That's about it these days. Major behavioral issues go to the office, but I can't send kids down there for smaller issues. A consequence of "calling your parents" isn't always a consequence for some kids if their parents aren't going to do anything about it, so that isn't a reliable motivator or equitable consequence for all kids (one kid's consequence may be a two-week grounding, while another kid has absolutely nothing happen to him for the exact same behavior).
I do think that most teachers who tweak grades due to behavior issues do it with age-appropriate behaviors in mind -- a kindergarten teacher isn't going to knock down a kid for fidgeting a little bit during a presentation. My expectations for students are VERY clear, so they know what types of behaviors may result in a grade penalty. My only question for this particular incident might be how/why the teacher decided on the grade of 2 out of 10. Was that related to the number of times the teacher warned the student to put that item away? Was there some type of activity the students were supposed to be doing that the student missed questions on...and behavior points were taken off in addition to that (so a video quiz worth ten points...the student missed seven questions...the teacher then took off another point due to behavior)? If all ten points were based solely on listening and the teacher arbitrarily took eight points off, that would be little tougher to understand. I could pretty easily justify taking off 20% of a grade for something like that, but not 80% off. However, with my "parent hat" back on, I still wouldn't raise THAT issue with the teacher if it's a one-time thing and it didn't completely devastate the kid's final grade in the class.
You noted that you were offended by the "bad behavior in class" phrase being used to describe your daughter's issue, but keep in mind that if you found that as a comment attached to the grade in an online gradebook system (and it sounds like that may have been what it was since you didn't contact the teacher directly) the teacher may be limited to a certain number of typed characters or may be limited to a list of system-generated comments and have to just choose one from the list. I wouldn't let that "label" bug you too much.
There are some schools (especially high schools) that are moving to a system where grades are very clearly based only on a student's mastery of the content. Points can't be taken off for late assignments or unexcused absences or other behavior issues. Points also can't be GIVEN for non-academic things (like extra credit points given for bringing in a canned good for the school food drive or for showing up to a school event). I'll even heard of schools where points can't be taken off for CHEATING -- the student has to be given an alternate assignment to be able to demonstrate their mastery of the content, and the cheating behavior is addressed in a separate way. I guess I can understand keeping a tighter rein on things in the secondary setting where GPA when compared to other students can actually MEAN something, but I don't think having a behavioral component to grades in the elementary setting is a problem.
