The reason that the betas were ungeared and then regeared is as follows.
We need to share/equity beta to get the cost of equity. However, because the gearing of the company is changing (due to the redemption) the risk of the share (and therefore the equity beta) will change. This will mean that the cost of equity changes.
So……if we know the current equity beta, we need to ‘remove’ the existing level of gearing (by degearing) and then replace by the new level of gearing (by regearing).