How can one reconcile not pardoning a small amount of impurity from urine and feces with the absence of an obligation to insert a finger into the anus when performing istijmar, while ensuring the removal of impurity with tissues without inserting a finger?

It is not obligatory to remove impurities from the inner part of the anus. Rather, their removal becomes obligatory if they reach the status of the apparent, such that water can reach them. Scholars have warned against tampering with the inner part of the exit, stating that it is impermissible and a source of whispers (waswas (definition)). Everything that water cannot reach is considered internal, and internal excrement does not acquire the ruling of impurity until it exits.