Why would a convertible bond be less sensitive to a change in interest...

The convertible bond’s market price is affected by rising interest rates as are other bonds. However, if the underlying stock is also rising, that will tend to cancel out the effects of rising interest rates for a convertible bond. After all, whatever the underlying shares to which it converts are worth determines the market price of the bond, regardless of interest rates. If the bond converts to, say, 20 shares of stock, it has to be worth something at least close to what those 20 shares are now worth.