The former Lincoln City boss was seen to march towards the area of the banner as the players left the field of play, with fans gathered at the bottom of the stand.
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NCM's Paul Smith and Gary Moss were both present at the game and could see what happened but only from a distance, but spoke to one of the fans who Thompson had an exchange with.
He said: "He just came over and asked why we want him out.
"One person said 'because you are killing the club,' and Thompson replied 'If it wasn't for me you'd be in the Conference now'.
Captain Jason Lee was forced to take Thompson away and was seen to raise his hands at the gathered fans as if to either say sorry or that's enough.
It is not thought to have involved any bad language.