Hello Maureen,
Here's my reply. In order to achieve this, firstly you have to make a copy of your CRM_NewActivity screen. Then when you edit the screen, Go to Hidden Section, under that section you will find a Hidden Function Button.
Click on edit on the Hidden Function, and go to Step 2 of 3:Button Actions and look for Send Email action in the list. Once you find the Send Email action click on edit.
Remove the value from Email BCC action result, save and close it, Publish the screen and try to assign an activity and test it. I have test it on my account and it is working fine.
Hope this helps,
-Inder