It goes between the headphone jack housing/GPS antenna housing and the hole in the case supporting the whole assembly, where the middle of the three 1.8mm screws attaches to the back case (step 19). The order top to bottom is screw, metal part of housing, washer, back plate. Hard to explain, sorry.
I too managed with just heat (iOpener that had come with parts for another repair) and the plastic card. I decided to try with just heat because of concern about putting any fluid into the computer case. (There was a comment by someone about damaging a trackpad). Using the card and heat, I found it helped to start by inserting and advancing a pointed end of the card rather than an entire long-edge of the card. Then advancing the card, while also moving it in a back-and-forth motion, to essentially “cut through” the glue strips. One other point, that helped for later positioning the new battery so the the speakers fit without issue, was that with a sharp pencil I traced the outer edge of the old battery on the inside of the case. This left a nice aid for worry-free placement of the new battery.
Pay careful attention to the orientation of this plate so that when it comes to re-installation you put it back the correct way. Sounds obvious but I’ve found it inverted in one customer’s phone, which led symptoms of charging failures and repeated spontaneous restarts.