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If you're willing to live with a tiny amount of image distortion, here's a quick shortcut that gets you 80% there.

• Copy your drawing to a new layer, so that you have two identical layers.
• On the top layer, change the layer blend mode to Lighter Color.
• Now activate the Move tool and move the top layer two clicks up using the up-arrow key. (Alternatively, you can move it two clicks down—either will work and it's your choice.) The blend mode of Lighter Color compares the brightness of each layer and keeps whichever pixels are the lighter ones. In your case the lines on the paper are generally darker than what's around them, so the blend mode will replace the dark lines with the lighter colors.

Here's what I get after doing this, at 300% magnification. You can still see the ghosts of where the lines were, but not nearly so bad as what you started with. From here, you can use the clone stamp or spot healing tool to clean up the image further.

Edit:  you can now eliminate even more of the ghost lines using Surface Blur. 

• Copy the combined image (after following the steps above) to a new layer using Stamp Visible (Shft+Ctrl+Alt+E).
• Go to Filter>Blur>Surface Blur. You can experiment with the settings, but try using Radius=1 and Threshold=10.
• If you want, you can apply a layer mask to this blurred layer and brush it in selectively to the spots that need it most.
• See final image down below.

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