Does tayammum lift ritual impurity when water is unavailable or cannot be used, such as due to illness, according to those who hold that it does lift ritual impurity?

Scholars differ on whether tayammum (dry ablution) removes the ritual impurity (hadath). Most of them hold that it merely permits prayer and does not remove the hadath, because it is a necessary substitute. However, the Hanafis, some Malikis, Shafi'is, and Ibn Taymiyyah hold that it does remove the hadath, citing the hadith: "Pure earth is the purification (tahur) of themuslim," and the verse: "but He intends to purify you," arguing that "tahur" (purification/purifier) is the name of that which purifies, and thus the hadath is temporarily removed by it and returns upon the availability of water.