Hi @asquyres,
It looks like you're putting JSON with postman, so I think your format just needs to be tweaked a bit. Try:
{
course_section:{
'start_at':'',
'end_at':'',
'sis_section_id':'',
}}
just put the right values in for each of those (I couldn't copy/paste from your screenshot or see it while I typed this, but I think this may give you a general idea of what to try. I discovered this when I did my CCTA API class last year, as I was already familiar with API with other things like Python and had run into similar issues there.
I hope this helps, but let us know if you still have any difficulties!
-Chris