I've observed this now with a couple versions of SSR and in varying environments; 2011 and 2013 R2 so far, and I see a few other posts discussing some very poor network performance on the part of SSR.
I had to move some recovery points (19GB) from local attached storage to a network share using the Move Backup Data function under Manage Backup Destination. This process has taken several hours over a Gb network link with low latency. Task Manager/Perf Monitor show NIC utlization barely goes above 1%, in fact it's often 0.6% to 0.8% on the source server.
Current environment: SSR 2013 R2 on a 2008 R2 server (2Gb teamed NIC), moving data to a network share on another 2008 R2 server (single Gb NIC). If I copy a random file using Windows Explorer from the same source disk to the same destination share the NIC utilization goes through the roof and almost maxes out. Why is SSR chugging along at a snail's pace?