This page will explain how to change the transparency of the basemap in a web map in ArcGIS Online
Navigate to the desired Web Map and press the "Item Details" button
Click Open in Map Viewer
See the Web Map with a visible background image (Basemap Image Layer)
Click the Expand Arrow
of the Basemap Imagery Layer Group to show the Basemap Layer(s)
Note: This example uses the Dark Gray Canvas Basemap Imagery Layer Group, which includes the Dark Gray Reference and Dark Gray Base Layers.
Click More Options
found under the desired layer
Note: This example shows the Dark Gray Base Layer.
Click or hover your mouse over Transparency
Set Transparency to 100% for any basemap imagery
See that there is no longer a basemap present