Fourier transform of $\sum_{n=-\infty}^\infty(-1)^n\delta(t-nT_0)$
HINT:

Note that the given $h(t)$ can be written as

$$h(t)=g(t)-g(t-T_0)\tag{1}$$

with some $g(t)$ the Fourier transform $G(f)$ of which you know. So from $(1)$ you then get

$$H(f)=G(f)\left(1-e^{-j2\pi fT_0}\right)\tag{2}$$