Adicione .* a p em sua primeira linha.
Experimentar:
DELETE p.* FROM oc_product p
INNER JOIN oc_product_to_category pc ON p.product_id =
pc.product_id
WHERE pc.category_id = 343
DELETE p.* FROM oc_product p
INNER JOIN oc_product_to_category pc ON p.product_id =
pc.product_id
WHERE pc.category_id = 343
