I fixed the same problem on my MFC-7860DW with ordering that small plastic part above from China on Ebay (less than $4, took 1 month to arrive).
I followed this video to put in the plastic part:
https://www.youtube.com/watch?v=zcZ5gF0t7Kc&list=FL4L05E9M8WEKm3gAgvTigLw&index=1
The only thing not clear on the video is that you have to put the small hook part into the notch so it can function well. Tried a few tries to understand. The view of the fixed piece can be seen from tray side like this:
https://drive.google.com/file/d/13ojo4LDvgB3BW7ZG8NAu48rkautrQ5ju/view?usp=sharing
Thank you for your information!