If you negotiated 20% higher starting salary then you earn 20% more for the same work than the person who didn't. I don't know of many companies where you can't negotiate for a 20% higher starting salary so I don't really think this would cause a large reputation hit.
The primary way you negotiate a higher salary at your current place of employment is to either go work someplace else or threaten to go work someplace else. Actually going to work somewhere else is the far more likely method for most people. Either way you are no longer working at the place where they didn't value your work enough.
