I assume they are capacitors (forgive my ignorance) but the same one each board is broken and 2 more on each board are loose. 1 and 2 from left to right in the image. Same on both boards...
Uh, without reflowing it's hard to resolder them. That's from my own experience with the boards from Mr. Teal.
Maybe it is possible with a preheater and leaded solder paste. Also with unleaded solder paste but then with higher temperatures....
I had this same problem with one of my Technobit Chilis. I wasn't able to reattach it directly to the board.
Instead I made two wire extensions using some 26-ga copper from a piece of cat-5 and soldered them to the board. I used 2 irons at once, a 25W and a 30W to get the solder to melt. Then I soldered the cap onto the extensions.
It's not pretty but it works.
I guess I could have left the black plastic piece out, but I didn't want to lose it so I stuck it in there.
I should probably wrap some tape around the cap body so it doesn't short against other things on the board.