What is the ruling on entering a mosque with shoes that have been used for ablution (wudu') and are thus impure, in an area of the mosque where there is no carpeting, knowing that this area might be carpeted during overcrowding?

We have been commanded to exalt mosques, honor them, and purify them, for they are the houses of Allah. And whoever exalts the sacred ordinances of Allah – it is better for him. The Prophet, peace and blessings be upon him, forbade any filth or urine in them, and he informed that removing dirt from them is among the acts of reward. Therefore, it is not permissible to walk with defiled shoes inside the mosque as long as it is designated for prayer.