The "checkerboard" indicates a transparent area. You can only have transparency in a "floating layer" which is marked as Layer 0 (or any number).
If you cropped out the surrounding area, you deleted those pixels. The checkerboard shows there are no pixels and the layer is a floating layer "Layer 1"
It's kind of fun in a way. You can place the object over another layer, another color or photo, and see what it looks like.
They are not on about the transparency. If you look closely at the center of the image you can see a grid across it.
Op I'm not sure what's causing that to happen, but will try to find out for you.
Those? They look like "Guides", used to align objects. View menu > Clear Guides should work if they are.
The OP posted two screen captures of Photoshop displaying two different document the first a Document just open from a Jpeg file. So a single Background layere no transparency and no grid. The History Palette shows this as the Layer palette is hidden.
The second Document was opened from a Layered PSD file. Can not tell how many layers or what the layer structure looks like or what kind of layers or layer contents for the layers palette is hidden. The history palette show the open then a drag selection. Have no idea how the selection was made. Then there was a move followed by a delete layer. A paste, have no idea of what was in the clipboard. Then a move followed be a second layer delete. Then a layer may have been dragged in moved and deleted. A brush stroke added then backed out by stepping back in history. If the document has a background layer its visibility is turned off for the composite displayed has a transparent background. Seen in the composite is a grid over some part of an object but not all of the object and not over the transparent background. What layer or layers the grid is in I have no idea do not know if the gride is in a layer of it own.
May be a Photoshop Grid but viewed at 100% zoom as captured the grid does not look very good or look like it is covering part of the right side of the object. I could be wrong foe it also looks like the fulls size capture has been scaled down in size.
And what exactly has this to do with the grid on the cropped image? You post is nonsensical and absolutely no help.
I'm going to suggest you stop posting this dribble and try to be more productive in your replies.
gener7 Suggestion makes sence and worth a try.
thaliaa1428409 Can you post back if this cures your problem?
Without seeing their layers palette all I could see is what was shown in their history palette their dribble and it made no sense to me either. The screen capture was also scaled down in size and I could not tell is the lines were guide lines or a grid or in the image. When were you appointed judge jury. Your new here....
If they are Guide lines they use the view menu to clear canvas guides.