How will the Ledger Half Custodian SegWit2x coin split work?
Relevant info in this answer: https://bitcoin.stackexchange.com/a/62134/51948

A tainted input is referring to an input which is only valid on one chain, not both. Such an input can be created by mixing some coins which were mined after the fork in, making the transaction and all its children invalid on the other fork, and thus allowing those transactions to be further used for splitting other coins too.

It sounds like the "contract enforced by the new application" just means that the ledger application will only sign transactions which send their inputs back to themselves, it isn't just going to let you spend their inputs as well and give you free coins.