Customer Activity Screen and Deleting Items

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Hi all,

We have 3 users who access our accounts, and we use Remote Desktop Connection. 

One of the users, our credit controller,  if they go to Customer->Activity screen does not seem to have the Delete button at the top.

However, if they go to Customer->Customer Record->Activity  then they do have the Delete button, which seem very odd.   Is there a setting where I can add this?

Also, it lets me delete items from the Customer->Activity screen, even when others are logged in.   But if I try via the Customer->Customer Record->Activity then it wont let me as other people are logged in. Is that normal?   Again it seems odd that the 2 activity screens would be different. 

Any help greatly appreciated! 

Paul