Fundamental Group of $\mathbb{R}^2-(\mathbb{Z} \times \{0\})$

Question

In Fundamental group of $\mathbb{R}^2 \setminus (\mathbb{Z} \times \{0\})$ it is said because $Y=\mathbb{R}^2-(\mathbb{Z}\times \{0\})$ has a countable points less than whole $\mathbb{R}^2$, then at each point we can retract the space into circles, and finally the space can retract to a wedge of infinite countable circles.
Could anyone elaborate this more? Thank you.