Yep, that part of the clip he removes the tape that holds the ribbon cable clip down. You can replace that with a small piece of scotch tape when you put it back if you want, but it isn't really necessary once the phone is closed up.
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At 5:21 he shows how to re-assemble the ribbon cable. That little white thing is the clip and it flips up from the back to the open position. My guess is you simply pulled the cable out and never opened the clip. If you try to push the flat cable back in with the clip closed, I doubt you'll get a good connection, if you get any at all. Open the phone up again and pop the clip up, then insert the cable all the way to the back of the connector and then push the clip back down to secure it. If you want the belt and suspenders, then use a bit of scotch tape over the whole thing.
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