Looking for the pit/s could be problematical as all traces in the area have vanished, and even where shown to exist all surface signs are obliterated. The steepest road leaving the village is the B1203 heading south westerly. The Ordnance Survey 6 inch to 1 mile Old Map (1888-1913)
clearly shows a couple of chalk pits and a marl pit close along the southern side of the road going to Binbrook top. In the village a couple of springs are labeled and a stream resurges on the north of the village flowing northerly

(So as soon as possible he dashed off to the "pit" where he knew they would make camp. Straight up the steep main road to his stand-point, a gate on the right-hand side. This led to a rough cart track on the edge of the field leading to the pit.)

There are a couple of tracks shown on the right. The first barely out of the village goes some distance towards the stream and a couple of fishponds. The next just outside Kirmond Le Mire leads to a hydraulic ram (presumably lifting water to the big house)and a stream. No sign of pits or quarries anywhere in the immediate vicinity of either track though.
However pits were ephemeral if dug for liming fields and the drift cover is variable over the wolds and I believe only the Gipping Till was calcareous - with the rest of the drift/tills the clay would have required 'sweetening' There are numerous circular features that can be seen on the satellite imagery. They could be infilled pits but equally they could be far more ancient features that ploughing has virtually destroyed. This was a far more densely populated landscape prior to the sheep invasion and the mention of a barrow on the map takes the history back several thousand years so residual rounded patterns could mean all things to all men. It would require boots on the ground and even that may not give definitive explanations. If you scroll back in time on the satellite imagery the crop patterns emphasize some of these features but do not explain them.
Apologies for a bit of a ramble but landscape archeology is a bit of a hobby for me.
I think locating the encampment/s is a bit of a challenge too far.

https://www.archiuk.com/cgi-bin/build_nls_historic_map.pl?search_location=,%20Binbrook,%20Lincolnshire&latitude=53.420157&longitude=-0.195756