"That's just part of it" vs "that's just a part of it"

Solution 1:

1. They are both correct grammatically, and they mean essentially the same thing.

2. To me, there is a slight difference in connotation:

   • part of it -- emphasizes/suggests an integral connection between the part and the whole; doesn't lose sight of the whole, while pointing out that something is missing without this part
   • a part of it -- emphasizes that there could be multiple parts, and the division into parts could be more or less arbitrary; emphasizes the part(s), perhaps losing sight of the whole somewhat; de-emphasizes any organic connection between the part(s) and the whole

   This difference in connotation is not necessarily what is meant in each case, or even in general. It is a possible difference, and thus a difference.

Solution 2:

I think it's more common for Speaker B to reply:

That's part of it.

However, I think that either one is grammatically acceptable. (I wouldn't be surprised to learn that it's a regional difference, but can't prove that.)

In case you were interested, both phrases (just a part of it, just part of it) are increasing in frequency, although the shorter phrase is currently winning out. Check out the ngram here.