I think the 'きて' here is only saying they came back with the gifts.
The nuance in English would be the same as:
"...bring back souvenirs for me(that they buy)"
"...buy souvenirs for me"
The difference is subtle. Both phrases can be used in the same context but offer varying degrees of detail. Not much different from how we use English.
For me, as a writer, the difference is more noticeable. With the ”きて” I can picture them giving the gift, I see expressions, I feel the joy, excitement. Without it, it's not that I get a negative impression but I might only picture them buying the gift. Different experience.