So as wildly underpowered as it would be, I've tilted toward a forest gnome warlock rather than a half-elf.
Comes from the Groaning Forest. Was never as clever as her fellow gnomes (flat 10 int after racial adjustments), so she made a pact with some fey entity in the forest to try and gain powers that way. Was not literally cast out, but it only led to further social ostracization, so she gave up and left to seek her fortune, and a sense of belonging, elsewhere. Port town like Bit seemed as good a place as any to start anew.