We have two LG mobile phones. The following message keeps coming up on both phones.
Couldn't sign in
you typed an incorrect password or your account has changed. Re-type your password. If you forgot your password and need to recover your account click here
Nothing happens when we click any of these and we can't get rid of it
Sounds suspicious. Is it popping up in a window on the screen, or is it coming in as a text message? If its comming in as a text message it may be someone trying to scam you guys, and they somehow go ahold of (or guessed) your phone number. If that is the case you can setup to block that person using settings on the verizon wireless website. If its a pop up from an app then you need to find out which app. If you go into Settings and App Manager you can scroll over to All and stop/disable any apps you don't use, or don't plan to use (you may want to leave the Verizon and Google ones enabled for the time being, so you don't loose any features, but you can experiment with them later to see if you actually need them all running or enabled).
If you don't already have a legitimate anti-virus/malware protection program on your phone you may want to consider the VZ Protect (also known as Verizon Support and Protect on the Google play store). If the message is being caused by a virus or malware that app should be able to spot and remove it.