Your parents may well have dug a considerable hole for themselves by extending their stay, even more so as it's been such a long visit.
We had a member recently on the forum who was later refused a visitor visa for exactly this reason. Your solicitor gave sound advice but you may have left it too late to write to the UKVI (the UKBA were disbanded in 2013). You should have contacted them before the 4 week period your parents originally requested had expired.
I wouldn't advise giving the reason for the extended stay as caring for their grandchild as the UKVI deem this to be unpaid work, which isn't permitted on a visitor visa. You could write and explain that you've only just been advised that your parents should have returned within the specified time in their application, but to be honest it depends on how the Entry Clearance Officer views the next application.
Edit: As per usual, beaten by noajthan