Definition taken from the Investopedia.com

What Does Tainted Alpha Mean?

An alpha return that cannot be attributed solely to the money manager due to consequential beta exposure. Tainted alpha is seen when money managers invest in individual equities, instead of using market neutral strategies such as arbitrage, and hedging.

Investopedia explains Tainted Alpha:

Due to many individual investors being unable to invest in funds that use pure alpha strategies (i.e. hedge funds), tainted alpha is common among the majority of managed portfolios. For most this is acceptable, because of the benefits of passively capturing gains that are associated with long term beta exposure, along with a money manager’s stock picking ability.