I've had good luck using a 19 or 20mm, 12 point socket to loosen the lock bushing (the plastic part in question)on Shimano pedals. The TL-PD40 is quite inexpensive (it, too, is plastic)--just a couple USD--so when you're able it's a pretty cheap investment. Locking pliers will work as well, but as others have mentioned, continued use of those will deform the bushing in short order.
It's helpful to insert the appropriate sized Allen wrench (6 or 8mm, depending) in the end of the pedal then secure the wrench in a vise. This will hold the pedal secure and also allow you to work on the bushing with both hands. On Shimano pedals, the lock bushing is left hand threaded on the right pedal. To loosen the lock bushing on the right pedal you would turn the bushing clockwise. Conversely, the left pedal lock bushing is conventional right hand threaded, so loosening it requires counter-clockwise rotation of the bushing. There's at least 30mm of fine threads on a lock bushing so it takes a lot of turns to free the axle assembly from the pedal body.
Once the axle assembly is free, you can clean it up to better view the bearings and their situation. At the end of the assembly are the 10mm cone nut and 7mm lock nut. You'll need to secure the cone nut while you loosen the lock nut. With the lock nut loose you can then turn the cone nut to set the bearing preload. You state your pedal is too tight, so loosening the cone nut would be the action necessary (if there are no problems with the bearing balls--missing or deformed typically). It's likely that the cone nut will need a 1/2 turn or less to get a better adjustment on the preload. There's a very fine window between too loose and too tight. Again, the threading for the cone nut/lock nut is RIGHT pedal--left hand thread & LEFT pedal--right hand thread.
Cleaned and greased the pedal should run smooth again.