Minimal Viable Plasma

I have a question about exited UTXOs. Please correct if the following understanding is wrong.

In Minimal Viable Plasma (ex. GitHub - omgnetwork/plasma-mvp: OmiseGO's research implementation of Minimal Viable Plasma), I think it seems that the child chain does not know which UTXO has been exited, because exit requests can be submitted to Plasma contract directly. So the operator should check exited UTXOs stored in the Plasma contract on the parent chain before accepting transactions on the child chain.