Basis Risk and Hedge Ratio

To accommodate differences between the Treasury bond and the CTD, a yield beta is calculated and the hedge ratio is multiplied. How is basis risk hedged?

Unclear how sentences 1 and 2 relate to one another in your post. However, it seems to say that basis changes drive the historical beta calculation. So if you hedge using beta, you are hedging the basis risk. Not sure how true this is in real life, so maybe I misunderstand the statement.