You are on the hook for a change fee + fare difference. Period. This is the outbound. Have there ever been waivers or errors by DL? Sure. But, don't count on it. So, start with the facts:

1. Read the fare rules. What exactly is the change fee?
2. Is your specific fare bucket actually available for purchase? If not, what is the next best fare?
3. Are you better off letting this ticket go, taking the credit and using it at a future time?

If this is work-related and your employer pays, I don't know of many significant businesses which would not pick up the costs associated with a change. Why not start there?