Buybacks "pumping the stock price" is a common misconception, but not actually true (unless the buyback is executed at prices lower than fair value).
There are less shares outstanding afterwards, but there is also less cash, so if executed at fair prices there is no reason for the stock price to move.
Just think through an example of a simple company which is a pot of $1000, and can get 10% returns on it. There are 100 shares, so if investors want 10% returns, shares should trade at 10$ (P/B = 1). If the company repurchases half the shares, there will be only 50 shares but the company only has 500$ now, making each share still worth 10$ for 10% hurdle rates.
There are less shares outstanding afterwards, but there is also less cash, so if executed at fair prices there is no reason for the stock price to move.
Just think through an example of a simple company which is a pot of $1000, and can get 10% returns on it. There are 100 shares, so if investors want 10% returns, shares should trade at 10$ (P/B = 1). If the company repurchases half the shares, there will be only 50 shares but the company only has 500$ now, making each share still worth 10$ for 10% hurdle rates.