A move could definitely confuse them a bit & make them temporarily stop laying. Also, their best egg-laying years will be the first two, so you should expect less eggs after that. Yes, if they get too many treats, they would be encouraged to eat less layer feed; although they don't have to have layer feed to lay eggs; they just need the extra calcium in layer feed to make nice, hard shells.
Since you got one today, you're probably right, and they're most likely back on track to begin laying again!