Hi,
There is no option to hide the field when printing.
As a workaround, we may set the font size of the field to the smallest size. To do this, open the draft message, click File > Print, under Settings, double-click Memo Style. In the
Page Setup: Memo Style dialog, under Format tab, click the second Font button under Fonts section and change it to
1 pt.

Hope this helps.
Regards,
Steve Fan
TechNet Community Support
It's recommended to download and install
Configuration Analyzer Tool (OffCAT), which is developed by Microsoft Support teams. Once the tool is installed, you can run it at any time to scan for hundreds of known issues in Office
programs.