I'm trying to find a short story about a woman whose job is processing time travelling refugees from a future genocide/dystopia. The protagonist is in charge of settling them in refugee camps. She's beginning to experience empathy fatigue, and she feels guilty about this. Some of the refugees have brought a device back in time with them to the "present", and she worries it's a plant from the future oppressors to try to hasten the development of the future which the refugees are fleeing from.
I may have read this in an Analog magazine.
It's older than 2010. Unfortunately my parents had an incredible library, so I'm not sure if it was from 2009 or 1970! I suspect it was from the 2000s but I'm not sure.