HubSpot has a feature that if mail is sent from HubSpot to any contact the sender will receive if an email notification if the mail is opened by the receiver in the mailbox.
But I had a doubt and wanted to know from you that what is the procedure you follow to open/create a task for the client. Since we can open/create tasks for only HubSpot users only. I guess you must have created a task for the HubSpot contact owner to send an email and then the owner sends the mail and marks the task as complete as a result, you're receiving notification that the owner has completed your task.
Can you please share a screenshot for a contact so that I can provide you a better solution?