How do I pause delivery to one pincode for a while without deleting it?

Go to Plugins → Delivery Restrictions and open the Pincodes tab.

Find the pincode in the list and click Disable. Its status changes from Active to Disabled, and shoppers entering it get your Not-serviceable message and cannot place the order. The city, delivery days and COD setting are kept.

When service resumes, click Enable on the same row.

Only use Delete if you want to remove it for good. Note that Bulk import skips pincodes that are already in the list, including disabled ones, so re-importing will not switch a disabled pincode back on.