How to remove Esri basemap credits?

Go to View -> Layout, then go to Insert -> Dynamic Text -> Service Layer Credits.

You should then be able to move the credits to wherever you want. (Or completely remove them)

Another option is to change the text color to "No Color", instead of moving the text box off the preview pane. This is useful when performing a graphic export and selecting the "Clip Output to Graphics Extent". Otherwise, the text box located off the preview pane will be included in the export.

I made a video on how to do it at YouTube

Go to View -> Layout, then go to Insert -> Dynamic Text -> Service Layer Credits.

You should then be able to move the credits to wherever you want. You can't delete it. If you do it will come back. So you need to move it off the preview pane.