Deleting W2 information with no dollar amounts from work in past years should not affect your refund or make you owe.
I would recommend revisiting your current year W2s by following these steps:
- Login to your account
- Click "Federal" on the left-hand side
- Click the "Income and Expenses" tab at the top
- Click "Edit/Add" next to Job (W2)
- Make sure all of your current year W2s are listed