This was my first time GMing and I made a really careless rookie mistake. I accidentally let one of my players start with a light repeating blaster rifle which I just noticed was restricted. We've only had one session so far. How do you all think I should handle this? I am thinking of offering to let her buy a new weapon and refund her the difference in credits. Alternately, I could let her keep the weapon, but remind her that since it is restricted she will have trouble carrying it onto worlds with strong law enforcement. They are on Nar Shadda right now so it won't be as big a problem, but if they head to more law-abiding world I could imagine it would cause major problems.

Let her keep it. At character creation she would have had plenty of time to acquire one.

Just keep regulating its use with common sense and you should be fine.

You should be fine. The weapon is basically unable to be licensed, so have her tie her obligation to that weapon. If it's rolled, even on Nar Shaddaa, someone threatens to call law enforcement and take her gun away unless his/her demands are met. Or perhaps an upstanding sector ranger happens upon her and requires that she "give up the weapon and come quietly." Lots of good adventure hooks there.

The Restricted LRB isn't really all that much more powerful than the completely legal Heavy Blaster Rifle. If you need to do a continuity edit, replace it with a HBR and throw another 750 credits back into his pocket.

You can start with anything as long as you're willing to take the Obligation.