Thanks for replying everyone.
Yes, this was a “Pit Stop” place; it’s a new section that’s connected to the proper big-chain mechanics section. Well, I did manage to get them to put in writing that the oil was overfilled by them, and the low transmission fluid was connected to their handiwork. They cldn’t deny the oil overfill, and would only admit the fluid level was low and had to be topped up, but I forced them to put in writing that their staff did it. So it’s in the work order sheet in very summarized format.
The trouble is, the foreman – who claims over 40 yrs of experience – denies that any short/long-term damage has been caused by this incident, so I wldn’t know what to do if my car has problems 1 or 2 months down the line because they will deny cause-and-effect. I’ll probably only be able to cause a stink by calling up the media.
My car is running fine now and no white smoke billowing out from the exhaust, and reverse gear is fine too. I had stopped the car immediately as soon as I saw the smoke and didn’t drive it again – I got it towed to the place – so I’m hoping that managed to keep any damage to a minimum. But as I’d smelled burning when the smoking started, I’m worried the transmission line or something else has already been damaged.