You can hide pivot object from toJson() method on the related model and tweak the relationship definition to have desirec column visible on the main model:

// Category model
public function products()
{
  return $this->belongsToManu('Product')->withPivot('desired_column as desired_column');
  // this way you override aliasing the column to pivot_desired_column thus avoid it being attached to the pivot model
}

// Product model
protected $hidden = ['pivot'];

// execution

$category->products->toArray(); // the same for toJson()
// array(
//   0 => array(
//     'id' => '1',
//     ....
//     'created_at' => '2014-04-10 19:54:30',
//     'updated_at' => '2014-04-10 19:54:30',
//     'desired_column' => 'some value from pivot'
//     )
//   ),
//   ....
// )