Is it permissible to swear that what is written in the trust deed is the rent for the retrieval of the outstanding amount?

There is no harm in swearing that the landlord is owed a certain amount by the tenant, or that he holds a trust for you amounting to this sum. This is considered a form of Tawriya (deliberate ambiguity), where you mean by "trust" what is owed to him from the rent, while the judge understands it as a trust other than the rent. Al-Nawawi held that lying is obligatory if the purpose is obligatory, such as concealing a Muslim from an oppressor, and that swearing an oath through Tawriya is obligatory.