The EGR solenoid regulates small amounts of exhaust gas.The EGR which means exhausts gas recirculation. You have a EGR valve that the exhaust gas run through ,is controled by the EGR solenoid allowing the precise control of EGR flow. Unless he ran a diagnostic check on your car, you might want to consider having one done. If you put a few dollars more of what a check would run you you can buy one of the dtc readers and it will give you a code which the better the dtc reader the more precise of problem with out doing a check its possible your cars not going into overdrive could be your evap valve, which that was what my problem was with my vehicle not wanting to go into passing gear. A good reference manual of your year vehicle that you can get at most parts stores can keep you from being taken for a ride.
It would be nice if people actually used punctuation when using the internet anymore. Anyway, the previous response was essentially correct, the EGR solenoid just recirculates exhaust gases to reduce emissions and keep the engine cool. If your car's overdrive system is vacuum controlled, which is not likely, a leaky EGR solenoid could cause faulty signal to the car's computer. Again, this is not likely because vacuum systems tend to be on older vehicles and are generally used for emissions more than anything else.