An error on Introduction to Algorithms 3rd edition about closest pair of points
Just the two lines before, (or last two lines of page 1040 if you want) say the following:

Observe that if a pair of points has distance less than $\delta$, both
points of the pair must be within $\delta$ units of line $\lambda$. Thus,
as Figure 33.11(a) shows, they both must reside in the 2$\delta$-wide

Meaning that if you want to be able to combine them after divide and conquer phases, you specifically are going to look within the 2-$\delta$ range. And this is why the first step is to remove all the points that exceed that limitation, therefore that they do not satisfy such constraint.
You want to keep only the points within that window-range.