DC component of a discrete filter
Here is a (working) link to a paper relevant to the OP: http://citeseerx.ist.psu.edu/viewdoc/download?doi=10.1.1.80.2334&amp;rep=rep1&amp;type=pdf

It looks like when they say zero DC, they mean "band pass filter" (see page 4). And when they say DC component they just mean frequency response at zero frequency. For instance, see Eq. (20) where they evaluate $G_b(0)$. That's the answer to your question: you can define the DC offset of the filter response as its gain at zero frequency.