Is there a single word that means expressing insincere kindness in order to draw attention to oneself?

Solution 1:

I would say this woman is "grandstanding"

Which is described by the MW as the following:

3grandstand : to behave or speak in a way that is intended to impress people and to get public approval.

I would add a qualifier like "subtle grandstanding" or "grandstanding veiled as consolation".

Solution 2:

Sycophancy comes to mind. In the self-seeking manner that is.

sycophant

a self-seeking, servile flatterer; fawning parasite.

Reference:
http://www.dictionary.com/browse/sycophant

A person who acts obsequiously towards someone important in order to gain advantage.

Reference:
http://www.oxforddictionaries.com/definition/english/sycophant