That is your Low/Reverse (rear) band... the band strut is the piece that fell out. You should be able to put the strut back in and adjust the lever (the spec usually involves tightening the adjuster to 72 inch pounds then backing off 3.5-4 turns... check your particular application!) This doesn't explain why the strut fell out? Anyway, stranger things have happened...
I used to perform a recall on the 4 speed versions of these transmissions... the procedure included removing and replacing the band lever and strut with the transmission in the vehicle... so there is no reason why you can't reassemble yours... after you reassemble and adjust the band lever assembly, check for reverse operation and engine braking in manual low... if you've got that, then you lucked out!