Hi Leona,
Firstly, please note that users in Lync for Mac by default cannot modify the contacts. Since you are unable to delete the contact under “People” in Office 365, I would like to confirm some information below:
1. Can you send us the related screenshots regarding that you cannot Pam from you contact under “People” in Office 365? To upload images, please click Use rich formatting and then select the Insert/Edit Media button.
2. Whether other users under your tenant are unable to delete their contacts from “People”.
3. Please create another contact and try if you can delete it from “People”.
4. Which web browser are you using? Please try using IE10/11 to see if there is any improvement.
5. Does the Lync client in Window work fine?
6. Are there any on-premises environment deployed in your organization?
Please feel free to share any updates when you have time.
Thanks,
Ran