Done it, all in my own head, as is my eccentric compulsion (...actually, I only do it to annoy trevor...) - took a flyer on HAT(e)FUL , so glad to see this endorsed by jazzgirl and grandpa gruffalo - but '...to avoid the centre' would suggest removing 'h' - not 'e' - which you've both identified as the removed letter - but which isn't the central letter of 'the'.
So....sloppy parsing by the setter? Or am I being dense? Or a fiendishly clever solution that none of us have seen with an 'h' removed to give *A*FUL ?
With his/her sloppy use of 'Native' (- well, (s)he is a fan of Noel Coward, whose MDAE is one of the jewels of the English language), I rather suspect the former.
Watched 'Pointless' tonight and 'The Gruffalo' is not on the list of books that every British child should have read by age 14. Nor is 'Treasure Island', 'Alice in Wonderland' or 'Wind in the Willows- although 'The Cat in the Hat' sneaks in. Great Expectations? A la Recherche du Temps Perdu? Finnegans Wake? Maybe; maybe not.
Where's the next generation of X-word pedants gonna come from?