I’m not sure if there’s a simpler way to do this but…
if you select all of the text that you pasted into DT and go to Format -> Highlight The entire document will be highlighted.
Next, select the desired text once again and follow the same path, selecting highlight once again, (or use the shift + command + L key combo) and all of the highlighting will be gone, resulting in a white background.
So…it looks like you have to change the highlighting copied from DA to "DT highlighting" and then remove it.
In other words, copy and paste into DT, select the entire document or set of text (command +A), then hit the command + shift + L key combo. The entire document is now highlighted. Once again select the entire document or set of text (command +A), once selected, use command + shift + L.
You can also use the color panel to modify background colors - just select the text, open the color panel, activate the "Background" checkbox and choose the desired color.