When you add the base map into the table of content (TOC) and want to export the map, then ESRI credit will be added in the layout. This credit takes away the quality and aesthetic of the map. So there are few ways to hide the credit text on the map. This tutorial is for version 10.2 and will work for any versions above 10.1.
1. In layout window, go to Insert > Dynamic Text > Service Layer Credits.
2. Then you will be able to move the credit anywhere. You can delete the text or move it outside of the layout window. When you delete the credit text and add data again or do anything with the map, the credit text will reappear. So the best option is to move the text outside of the window. Next option is to change the text color to no color, then you do not have to move the text.
3. Watch the video Tutorial to remove the ESRI base map credit.
4. Next option is to draw the box on the top of the credit text for the map title.