Do the prayers performed with tayammum have to be redone due to the impurity of the ablution area and fear of illness, or is it sufficient to perform many supererogatory prayers?

The questioner's intent regarding "tayammum (definition) because the place for ablution is not pure is not permissible" is unclear. If she meant that there is no pure place for ablution despite the availability of water, then this is not a valid excuse for tayammum, as the purity of the place for ablution is not a condition. In this case, she must make up all the prayers she performed without ablution. However, if she abandoned ablution due to harm from water due to illness, then she is not required to make up the prayers.