Why do Terminal Services employees need to work in human-Giftia pairs? Why is it that Terminal Services employees need to work in pairs of one human and one Giftia? 

Nothing they do as part of their jobs seems to strictly require the presence of specifically a human, nor specifically a Giftia. (And, I mean, given that humans and Giftias are virtually indistinguishable until near the end of the Giftia's life, what difference would it make, anyway?)
It is possible that this sort of pairing is for the preservation of human life. Once a Giftia becomes a Wanderer they start to act on instinct alone which sometime leads to violent confrontation. 

In the pairs the human is referred to as the "spotter" and the Giftia is the "Marksman". The Giftia are as close to humans as SAI Corp has been able to make with the current technology but they are not human. If one reads Isla's character bio its states that she "often has difficulty understanding how social situations work" this minor flaw could potentially cause a team of two Giftia's to miss a Wanderer if it's in the beginning stages.

The human is because overall the human will have more experience with human/android interaction so they will be able to pick up on the subtle signs that could start showing when a Giftia's time is almost up. 

Also having the Giftia there can provide a buffer in between the human and Wanderer, granted the Giftia is still limited whereas the limiting functions on the Wanderer are off. Terminal Services would probably rather have a Giftia injured in a retrieval rather than a human. 

This is a potential reason for the pairing of the two but I could be wrong, not much is stated as to why the pair has to be like that. ref from Plastic Memories Wikia