Here are the requirements for Teacher Certification in Massachusetts:
An image pasted from the latter link:
The examination in Massachusetts is called the MTEL. To prepare for it sufficiently (especially in teaching "elementary" as opposed to "early elementary") I can speak to the two course sequence at a particular teacher-education program, that of the Boston University School of Education (where I previously worked as a postdoc and have taught both of these courses):
Even in Massachusetts, there are a range of alternative paths towards teaching (depending, for example, on the needs of a particular school or school district). Looking to the United States as a whole, the number of possible paths to teaching elementary school is finite, but barely so.
You may have better luck homing in on a particular school, and investigating how the teachers presently at that institution were prepared (as well as the sort of ongoing professional development required/attended). Your final two questions, if answered literally, will do little to provide insight into the planning/implementation of outreach activities.
What would be the minimum highest level math course a person in that profession would have to have taken?
Across all possible paths: None.
What would they be likely to remember, mathematically, from when they were in college?
This will vary tremendously, as some elementary school teachers were math majors, some were math education majors, some were education majors with a focus on math, some were education majors who did not focus on math (and may not have completed any relevant coursework), and some may have majored in something unrelated to math or education.
I suggest that you interact directly with a potential site for outreach and the teachers who are working there, and go in with an open mind and a sincere belief that the teachers want what is best for students - even if, in practice, this leads to actions that may appear as irrational from the perspective of someone outside of the institution of k12 education and its associated structures/requirements.
For more information about how some elementary school teachers are honing their mathematical craft, search Twitter for the MTBOS (Math Twitter Blog-O-Sphere) or iteachmath or tmwyk (Talking Math With Your Kids) hashtags, or check out Tracy Zager's book, "Becoming the Math Teacher You Wish You'd Had: Ideas and Strategies from Vibrant Classrooms" (Amazon, Google Books).