Yes, you can use ADD ROW to get the task back to say the Jan 1 week and enter time for Jan 3. The Task start date on the resource’s Task page again is Jan 3. However the planned hours do not show. The only way to get the planned hours to show is to delete the actuals for the task and then voila the planned hours appear.
Net, Net work around … If you only entered a few days of hours then take them out and then restart from the Jan 3 to enter time going forward. However if you entered a few weeks’ worth, then use the Add Row option.
However it still is strange to me that the Start Date is changing in the first place.