The screen stays black-white, but there are tools that allow you to change your colors export in an exported pdf to the colors you want.
You can export your pages as svg and edit this (e.g. with a text editor) to replace all added artwork with the fill color of your choice. Each SVG is basically just a text file with markup that describes all the line items in the artwork - and it appears that reMarkable exports the base layer as one segment, and the layer on which you have marked the papers on another grouped layer - but you don't need to worry about that, all you need to do is change its colour.
You can use an editor like Sublime Text 3 (is free), then go to View > Side Bar > Show Open Files. Then drag all your exported SVGs into that sidebar, thus opening them all in tabs. Now all you have to do is one simple thing to change all the layers colors that you added to each file. Press Ctrl+Shift+F (or Cmd+Shift+F on a Mac) - this does a global find and replace on all open files - enter exactly as below:
Find > fill="#000000" Replace > fill="#ff0000"
Here is chosen to use red (#ff0000), but you can change this to any hex color code you want. Then click Replace - you should get a message saying “replace X occurrences across X files” - just click yes! Now go to File > Save All And you're done! All your marked layers are now lovely RED.
This is faster than doing it manually in a terminal.
sed -i 's/#000000/#0000FF/g' file.svg