Taking the pawn back is not really necessary. I would just develop my pieces, using the fact that black cramped his own position with the bishop, and then open the position up at a convenient moment. For the precise move, I would just play 4. Nf3 and 5. Nc3, or something like that.
Do you know this line of QGA?

Bxc4 loses a piece after Bxc4 Qa4+ b5
Black can keep the extra pawn for a while with moves like Be6 and c6-b5 but if white ignores it he can control the center and get a big lead in development while black awkwardly is tied to the pawn's defense.
This game gets messy, but look at the position after black's move 8. White has 3 pieces developed, he's castled, and he has a pawn in the center. Black has 1 piece developed. White's general idea is to attack black's queenside pawns with pawn breaks like b3, a4, and even d5. White is down a pawn right now, but the entire black queenside is under threat due to far advanced pawns and no development to support them.
In the game white plays b3 right away and gets a queenside passer, pressure on c6, and no counterplay for black.
.. although me just saying this and showing you a game probably doesn't make you feel any better about it It's good to be materialistic, but don't be afraid of positions like on move 8-9 of this game. Black is the one who is afraid there, white has many good ways to continue the game from there.
Thanks. It is interesting that I cannot find this move in my books, although it seems that rather strong players are defending the pawn with the bishop. I always though this is something for beginners (okay, if I how Wang crashed Black, it is a line for beginners ).

Taking the pawn back is not really necessary. I would just develop my pieces, using the fact that black cramped his own position with the bishop, and then open the position up at a convenient moment. For the precise move, I would just play 4. Nf3 and 5. Nc3, or something like that.
Seems reasonable to me. I was probably too materialistic playing this line. Okay, I know the concept of a pawn sacrifice to have positional compensation, and I will keep this in mind next time I see this line.

I now from several books that 2.e3 is not so great because 2...e5, but it is a recomendation in some books and as far as I remember it was also played by Magnus.
For sure, White has a isolated d-pawn, but Black is behind in development and I would certainly like to play White here. Or what do you mean?

I now from several books that 2.e3 is not so great because 2...e5, but it is a recomendation in some books and as far as I remember it was also played by Magnus.
For sure, White has a isolated d-pawn, but Black is behind in development and I would certainly like to play White here. Or what do you mean?
Or is there an improvement for Black in this line that I am not aware?

This is one of my own games with the same idea. I vaguely remember reading about it somewhere. The move is very passive, so it's not very dangerous. I reclaimed the pawn with an even postion, but soon I remembered the Ng4 plan is much better and you get a great position out of the opening.

"I know you will probably complain that I had black and that it wasn't the same opening. But hey, he played Bf4-e3, wasting a tempo. So the position is the same."
It is the same idea for sure. I know bishops having a similar function in other openings, like the Grünfeld (with Black) or (I think) in a line against the Tarrasch. I faced in the QGA this line when I was climbing up the latter around 1200 or something, but better players seems to avoid it.
1. d4 d5 2. c4 dxc 3. e3 Be6
Books do not consider this. How do you play? 4. Na3? Or take the c pawn with the bishop and regain it after 5. Qa4+?