My son drove the car at about 40 MPH and the timing belt broke. I am trying to decide whether to scrap her or not.
It depends on which engine you have. The 2003 Mitsubishi Gallant appears to have been offered with both a 4 Cylinder 2.4L Engine, the 4G64, which had three variants:
Dual Overhead Cam 16 valve, Single Overhead Cam 16 valve, and Single Overhead Cam 8 valve.
The 16 valve engines are interference, but the 8 valve engine is not. https://en.wikipedia.org/wiki/Mitsubishi_Sirius_engine#4G64
The V6 3.0L engine offered in the gallant appears to have been an interference engine as well.
As Paulster2 said, it's impossible to tell based off of just vehicle model if your engine was interference or not.
As the others have said, it's almost impossible to tell the condition of the engine unless you can visually inspect the valves/pistons. However, I wanted to chime in because I used to own a 2001 Eclipse which used the same 4 cylinder engine as your Galant and had the same thing happen. To answer your question before my anecdotal story - yes it is an interference engine.
My timing belt disintegrated at 115,000 miles, the dash lit up and the car turned off. I pushed it to the side of the road and saw the remnants of the belt in the road. Took it to the shop and they simply slid another belt on and started it up and it was perfectly fine. This isn't to say that you may not have problems, but there are situations where an interference engine can survive that.
So long story short, get it checked out - you may get lucky like I did.