I am looking to move servers currently backed up remotely by a server running BE v12.5 to another server running BE v10d. Are v12.5 Remote Agents backward compatible to v10d?
Nope
You could try calling support and have them generate v10d serials for you after giving them the v12.x serials
Veritas used to do this (generally only one or two levels back, tho and v10d went End-of-Life May 6, 2009)