No easy way to contact them without creating an account on their website – or possibly twitter.

Maybe a very local search and warn if a duplicate?

?

Sometimes you just have to walk a footpath in both directions to get a true idea of the way it "runs" by following the signs. And of course if you've recorded the definitive first section on OSM it makes it much easier to "join the gap" walking the other way. I've found footpaths going through open gardens, through a garden hedge -- even through a doorway that mysteriously appeared :-)

But, if there are no signs on the ground -- then you are out of luck.
Although, even if there are signs, it doesn't mean that the path itself will be traversable.

May be wrong -- but it looks like there's very few routes in to Grimsby without using a trunk route. Perhaps those aren't suitable for walking / bikes?

Cheers,
Neil