In 40 moves, free 4 birds. Always when the objective is a low number such as 4 or 2 is when you know there’s some funny business down the road. In this level, there’s only one thing to be careful of, and that is the laddered square in the top right grid. If a bird lands on that spot, then only a convenient match nearby where the bird is swiped diagonally with a gift, will be able to return the bird back into the flow. Also the grids are connected diagonally, so anticipate accordingly.
Of course instead of wasting turns trying to get it out, you can always use the Grappling Hook.
Other than that spot, just be careful with the gift distribution in the final grid as birds can often become stuck a row just before freedom if there isn’t a nearby match. Use striped gifts in other grids to clear through rows of random gifts.