The centre of a finitely generated strongly verbally closed group is almost always pure

The assertion in the title implies that many interesting groups (e.g., all non-abelian braid groups or ${\mathbf{S}\mathbf{L}}_{100}(\mathbb{Z})$) are not strongly verbally closed, i.e., they embed into some finitely generated groups as verbally closed subgroups, which are not retracts.