Transfer function of open loop system
If you consider $X(s)$ as the only input of the system then the transfer function only exists for $T(s)=0$, and it is given by $G(s)$. Strictly speaking, with $T(s)\neq 0$, the system cannot be characterized by a transfer function because it is no longer linear. Note that a linear system must produce an output $Y(s)=0$ for $X(s)=0$. However, this is not the case for $T(s)\neq 0$.

You could also treat that system as a (linear) multiple input single output (MISO) system with two inputs $X(s)$ and $T(s)$. In that case there are two transfer functions:
$$H_X(s)=\frac{Y(s)}{X(s)}\Big|_{T(s)=0}=G(s)$$

and $$H_T(s)=\frac{Y(s)}{T(s)}\Big|_{X(s)=0}=3$$