There is only one field that exports in the standard gift history export or the gift acknowledgment export and that is the Fund Comment field.

This field is found on the Fund 2 tab in the Fund Module and is the first radio button labeled "Comments".

In the export, the column is labeled FundComment1, FundComment2, FundComment3, FundComment4, FundComment5 for each of the 5 possible funds you can have with a gift.