e.g., If you have a Contact custom field named "Unsubscribed," you could filter out unsubscribed Contacts by adding a filter in your Smart View.
b) A more permanent solution is to remove/delete that address from the Contact info. You might choose to save that deleted email in another custom field for future reference.
This will not affect emails that have already been synced (they will remain visible). It also will not affect other data saved on the Contact (phone numbers, other email addresses, etc.).
c) If you only have one Contact per Lead, you can also create an "Unsubscribed" or "Do not contact" Lead Status (under Settings > Statuses & Pipelines) and move that Lead into that Lead Status, so you know not to contact it at all. You can also add a filter to remove the Leads in this status from your lists.