corliss, WELCOME TO THE FORUM!!!
the capped honey frames, did you treat your bees while you had these supers on? the syrup, are these in the frames? is it capped? did you treat while you had syrup on? what miticide did you use?
can better answer your question, but in general, and in my opinion, any colony treated with miticides with supers on or contain capped honey frames that may have miticide residue in them is not fit for human consumption.
yes, you need to remove these otherwise you will have all sorts of pest problems. i do store deep frames of capped honey (not syrup), in a very cool, dry outbuilding, in extra boxes with tight fitting bottoms and covers. you can also use a plastic tub with a tight fitting lid in a cool dry area. you can use these to feed back to the bees at some point unless you treated with a miticide with them on, then i would not use these as feed to the bees.