Why not pay out a special div .of $.75 of undistributed income plus the reg. $1.25 div and still have $.78 left divided by 4 q =$.195 added to the $1.25 =$1.485 div per q give money back to the shareholders.
The fallacy in your logic is that AGNC no longer has ~$1.50 in undistributed income. They have already announced (and commenced to buy) a stock buy-back valued at $500M --- almost all of the undistributed income. That stock buy-back becomes an expense against earnings at the end of the year, so that the remaining undistributed income will be near zero (and no income taxes will be owed).
Management decided that it would be in the shareholders best interests to spend this undistributed income to buy back AGNC stock (increasing book value) rather than issuing a special dividend (which reduces book value).
The buyback has no effect on earnings. It reduces cash, capital and shares outstanding. It does have the effect of increasing the per share amount of undistributed income due to fewer shares outstanding.