I paper-filed by 8038-cp return. Can I amend it using your e-filing software?

No. If your previous 8038-CP return was paper-filed, the amended return must also be paper-filed. The same rule applies to electronic filing.

While amending your Form 8038-CP, you must provide an explanation for the amendment in a separate document labeled "Explanation for Amended Return." You will need to attach this document to your amended 8038-CP return.