ArcGIS Pro has the same capabilities as ArcMap. We give you the option to remove the service layer credits (SLCs) that appear in the map frame so you can place them somewhere on the layout rather that having the credits potentially obscure the content in the map. Keep in mind that those credits are there for legal reasons. Removing them from the layout or making the text transparent, etc defeats the purpose of the credits. They should be on the layout.
Steps:
1) With the layout view active, select the insert tab.
2) Within the Text group, click the Dynamic Text pulldown control
3) In the Layout section, click on Service Layer Credits.
This will extract the credits from the map frame and place the same information into a paragraph text element on the layout. If you have multiple map frames with different basemaps, all credits are concatenated.