The best way to move a content block from one page to another is to copy the content block to the destination page, confirm it is pasted to that page and then to delete the content block from the 'old' page to remove it.
Go to the original page and hover over the content block that you need to move.
Click the gear.
In the box that shows, click the "Duplicate Content Block" option.
A box will show that says, " Copy to Another Subpage" - select the page where you want to put the photo gallery.
Click "Save Changes" at the bottom.
The builder should bring you over to the destination page. Check to make sure it's there.
Then go back to the home page and delete the original contact block.