What is a "jump response" of a filter?
It's a bad translation of step response, i.e., the filter's response to a unit step $u[n]$ at the input. Note that the step response is the convolution of the unit step with the filter's impulse response:
$$s[n]=\big(u\star h\big)[n]=\sum_{k=0}^nh[k],\qquad n\ge 0\tag{1}$$
where I've assumed causality, i.e., $h[n]=0$ for $n&lt;0$.
From the given step response and Eq. $(1)$ it should be easy to derive the impulse response $h[n]$. You can also immediately draw a conclusion about its length. Then, by considering the symmetry of $h[n]$, I'm sure you know how to derive the group delay of the filter.