The problem is not related to Aspose.Words. Artifacts appear due to MS Word ambiguous handling of borders and shading drawn with white color. As a result the documents appear ok on print preview but produce artifacts during printing. To fix the problem you should avoid drawing cell borders with white color.
Here is an example of how you project code could be modified to that purpose:
' Apply top cell borders (if any).
If cssStyleInfo.BorderInfo.IsBordered(Border.Top) And Not cssStyleInfo.BorderInfo.IsOverridden Then
.Borders(BorderType.Top).Color = cssStyleInfo.BorderInfo.cGetColor(Border.Top)
Select Case cssStyleInfo.BorderInfo.sGetStyle(Border.Top)
.Borders(BorderType.Top).LineStyle = LineStyle.Single
.Borders(BorderType.Top).LineStyle = LineStyle.DashSmallGap
.Borders(BorderType.Top).LineWidth = cssStyleInfo.BorderInfo.nGetWidth(Border.Top)
If .Borders(BorderType.Top).Color = Color.White Then
.Borders.LineStyle = LineStyle.None
The similar code change should be applied for each cell border.