Gather the facts, double check your facts, follow the chain of communication established when the project started.
This decision falls into the lap of the project Engineer (who answers to the owner).
When the stuff hits the fan, you might find the contractor's finger pointing at you, even though you think you are both in agreement and on the same page.
Before you determine a fix on your own....
Before you decide on your own to hold the site bench or to hold the as-staked FFE, ask a few questions of people that might know the answers.
Ask the construction superintendent and the engineer who did the site design if either are aware of any reason why the building would have been staked 0.2' high. They may have made a field design change to correct a drainage issue, to meet minimum clearance of some underground feature, to get minimum slope on the SS outfall from the building, or one of several other possible reasons.
But if it was just a mistake in the staking, ensure that whatever fix you incorporate does not cause problems elsewhere, like ADA, drainage, ....
What you do as a fix depends on what's going on with the rest of the site. You are probably matching some offsite improvements at various places - SW, C&G, gravity utils (Storm & SS), so just adjusting all your staking to hold the FFE might be problematic when matching to these offsite improvements.
If it were me, I'd blend in the difference in as short a distance from the building as possible for hard surfaces. For dirt, I wouldn't worry about it unless the site is very flat.