What is the intention of someone who performed ablution, then touched their anus, and wishes to perform ablution again? And is the intention to remove minor impurity valid in this case?

Touching the private parts (penis or anus) directly, without a barrier, invalidates ablution according to the majority of scholars. The person performing ablution must intend, at the commencement of ablution, to remove ritual impurity, or to perform the obligatory ablution, or to make permissible what is not permissible without ablution, such as prayer, circumambulation (Tawaf), and touching the Qur'an.