An impulse signal is a signal that has a certain magnitude that is applied for a small time. So you can use transfer function block to model your T(s) and use sum of 2 step functions to create impulse signal input. Use scope or toWorkspace block to obtain the response.
Impulse magnitude = x
Impulse time = t
Step function 1: step time 1, initial value 0, final value x
Step function 2: step time 1+t, initial value x, final value 0