Is it permissible for a woman suffering from severe dark circles under her eyes due to anemia to apply a whitening cream to conceal this darkness and make its color match the rest of her face, not for adornment?

There is no legal impediment to removing dark spots permanently or temporarily by using a whitener or other treatment, so long as there is no harm to the user or an external impediment. This is based on the Prophet's (peace be upon him) saying: "There should be neither harming nor reciprocating harm." However, it is not permissible to use it if its composition or some of its ingredients contain an impure or forbidden substance.