How do I remove the grid overlay when viewing photos on my Nikon D5600?

Look for the word "grid" in the section of your camera's reference manual that covers how to view/review images on your camera after shooting them. Almost all digital interchangeable lens cameras have an option to turn on or off a grid pattern when viewing images on the camera's LCD screen.

If the issue you are describing is occuring when you're looking through the viewfinder to compose a photo, then look for "viewfinder grid display".

You can do two things:

First check if switching through the view modes when pressing up and down while reviewing a picture already cycles through one mode that shows the picture without additional elements.

Additionally, you can set the grid in MENU - Custom Settings (the one with the small pencil) - Viewfinder Grid Settings. You can also set the info you see in the viewfinder and the live view with the info button.

I have no idea why people thought it was necessary to edit the original question to ask something it doesn't ask. There was no mention of a grid overlay in the original question because no grid was being asked about. The "latitude and longitude lines" in the original question don't imply a grid, they imply the location information box (which displays the latitude and longitude)>

The solution is to use the directional controller in playback mode, as detailed in other answers.

The grid should only show up if you go into the retouch menu and select straighten. I'm not finding any other selection to cause that.