When I tried to download an image for the background (for the SETI graphics), I made a typing error in the URL of the image, and now it appears I cannot remove the erroneous transfer from the transfers section (tab). Is there a way to manually delete it or to reset all the transfers? BOINC continually tries to download the file but to no success because it doesn't exist.

Also, can you remove an image from the background of the SETI graphics? I tried clearing the URL in the SETI preferences and updating, but the image is still there. Is there a way to bring back the original background stars-flying-past type graphics?

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Try following:

go to "Your account" and to "Edit SETI@home preferences". There, choose as "Graphic preferences" the S@H Classic.
In the GUI, click on update. Afterwards, you can go back to customizing your graphics again.

Not sure it will work, I never tried using backgrounds in the customized one.

Good luck.