Oh man, that story and picture don't really leave me with a warm fuzzy feeling...
Is this on an XR2? If so, there are only ONE possible set of CV axles that would even fit. I fail to see how a "wrong" axle would still drive the car flawlessly but have this kind of issue. Sounds like some BS.
Those are not the correct axle nuts, still aren't, those are a generic Dorman axle nut. If that's what they threw back on there originally, that's the issue. It must be a locking OE-style stakenut. I don't trust their "fix" and as far as I am concerned, they ruined your axles by drilling through them.
The "Gear" you refer to is the hub & axle spline, they positively lock the axle into the hub (torsionally - the axle won't spin inside the hub but it can still slide in/out for service) - if that was ground up from everything working loose, a whole bunch of things would have needed replaced, namely the axle & the hub - the axle I'm not sure but the hub is definitely the old one (unless they sourced junkyard parts?)
Did they mention replacing the bearings or anything of that nature?
Good on them that they didn't charge you anything to "fix" it but IMO it looks like one hell of a hackjob. Personally I'm not sure that I would trust their "fix"... The correct parts ARE available and inexpensive (stakenuts!) this is cheap and lazy!