With $\sigma^2$ known, $X_1+4X_2$ is sufficient — the printed $T_1=X_1-4X_2$ is not, and is correlated with $T_2$

Let $X_1$ and $X_2$ be independent observations with $X_1\sim N(\mu,2\sigma^2)$ and $X_2\sim N(2\mu,\sigma^2)$. Suppose we define $T_1=X_1-4X_2$ and $T_2=2X_1-X_2$. Which of the following statements is not true?