The marks could be either field boundaries or tracks. That they line up with many features makes it very likely that they have some significance.
I read about the church when I saw a sign for it some years ago and wondered why it was where it was. Not every village church is in the centre of the present village, St Mary at Newington is a good example, only now are houses coming back close to it, the rest of the village is along the A2. Same for Teynham, and many others. Plenty of GTP opportunities
Meanwhile, here's one I prepared earlier. The building still exists, with pub signage, but it seems dead, or at least dormant.