Cheaper pedals are often set up too tight. Also grease is an excellent "brake" as far as spinning fast goes. If your new pedals feel smooth but won't spin I'd say leave them. You'll never spin faster than 90 rpm for long anyway. And the grease will damp the spin if you try to spin them much over that rate anyway. COnsider that a "flick" of the fingers with the threaded end on a dry pedal will likely spin the axle at around 150 or more easily it's a non issue if the grease holds them back at that speed.
Now if you turn the axle and it feels like the pedals are cogging then by all means loosen the cap and get something in there to loosen the retention nut by an 1/8 to 1/4 turn. That'll be enough to make them smooth. But it's not just the exposed nut. You need to remove that one and the washer with the finger that goes in the groove and loosen the nut BELOW by that 1/8 to 1/4 turn. Then put the keyed washer and locking nut back on and torque it down. If it's smooth then smile. If it's either sloppy or still tight then redo it the way you need to go.
If they are higher end pedals with sealed cartridge bearings then just mount them and ride. Between the grease in the bearings and the seals you won't get them any better and they DO loosen up and spin better after a few miles once they push the excess grease out of the way and work the seals into less of a death grip.