As long as you store the depth to which you are comparing on a probe, (i.e. both before or after the extension) there is no problem. Whether you are in check or not isn't path dependent. I usually store unextended depth, so that I can probe before having determined whether I am in check. So I have to subtract the extension from the depth when storing in the TT. If the TT contains the info whether you are in check, it might be easier to give the extension as the first thing you do, and only then start comparing depths. Then you can store the depth unmodified.
However, check extension can make search scores path-dependent. There is nothing to do about it. It does not harm, and anyway the effect is minor when compared to late move reduction.
Suppose Your engine played 1.d4 Nf6 2.c4 e6. Now 3.Nf3 Bb4+ 4.Nc3 and 3.Nc3 Bb4 4.Nf3 would be searched to different depth. When using transposition table, final score depends on which move will be searched first.
When using TT you can sometimes get extra depth through grafting. That doesn't have anything to do with check extension per se; there are many cases where you can get grafting without any checks. E.g. from the start position 1.e3 null 2. e4 will hit upon the position after 1.e4 if the latter was searched before it, and gain an enormous depth (2 ply plus null reduction).