Black tape over iPhone 4S logic board. What is it?

While refurbishing an iPhone 4S, I noticed that some tape had fallen off the EMI shield covering the Qualcomm MDM6610 chipset.

What I initially thought was some insulating tape was actually rigid transparent film with black coating on one side that could be removed using a fingernail.

Is there any purpose to this tape such as heat dissipation or EMI protection? What is the black substance coating the film, and is there any point replacing the tape as part of refurbishment? (The film had lost its adhesiveness so can't be reattached in its present condition).