Chosen Solution

ADDED THIS IMAGE. This is from the iPhone 6 logic-board replacement guide, step 23. The piece I am talking about is outlined in red. Its logic-board socket is circled in red. In the picture, the socket is detached. There is a part that attaches to the bottom (near the home button) side of the battery. It is shaped like a swimming dinosaur and attaches to the logic board. It came loose from its attachment, and then within the part, it came loose from its bracket. I am trying to figure out how to put it back together, as there is a small silver tab that I don’t know how to rebend. If I order a replacement, I need to know the name. If I want to try to repair it, I need to know the name to find out what it should look like when installed. My iPhone is my camera, so I can’t provide a picture. Below are two pictures of someone else’s iPhone (not the same model, but it doesn’t really matter here). Just concentrate on the area around the battery, not the circled part or other stuff. The black tape-y thing running along the bottom of the battery is the part that I’m talking about. You can’t see the continuation of the part in the pictures, but the part continues up (using the orientation of the first picture) along the right side of the battery, and then it jogs over to the right to connect to a socket in the logic board; it connects not far below – maybe a quarter of an inch – where the person’s finger-tip is pointing in the second picture. The up-and-down segment is stamped 820-5038-A in white lettering.

if you mean this then its the ribbon from the battery

You are best suited just buying a new battery all together. I’ve not heard of just refurbishing a damaged one due to the cost of replacement batteries starting out at about $10 up to $30 depending on battery and model.

This serial number refers to a iPhone 6 battery. Just replace the battery and you will be ok. It does not refer to anything on the logic board, you are mistaken.