The strange characters are likely the result of Access encountering characters in the string that are not part of the standard printable ASCII character set (32-126). The most common reason that I have encountered for this is embedded line breaks like the CR and LF that are inserted when you use vbCrLf in a VB Module. The same characters can also be added while editing a field by pressing Ctrl/Enter while inside the field.
I would agree with this and originally started down this line of thinking, but I thought this was more prevalent in exporting to something like Excel. Whereas Excel only has a, I think, LF, a memo field uses CR/LF so the leftover character would show up as a square in the export.
I talked myself out of this line of thinking because the user is an append query and I assumed from one memo field to another memo field - therefore an excess character should not be an issue.