  We use bordered Floer theory to study properties of twisted Mazur pattern
satellite knots $Q_{n}(K)$. We prove that $Q_n(K)$ is not Floer homologically
thin, with two exceptions. We calculate the 3-genus of $Q_{n}(K)$ in terms of
the twisting parameter $n$ and the 3-genus of the companion $K$, and we
determine when $Q_n(K)$ is fibered. As an application to our results on Floer
thickness and 3-genus, we verify the Cosmetic Surgery Conjecture for many of
these satellite knots.
