Blue smoke=oil (usually bad rings or leaking valve guides)
Black smoke=PARTIALLY burned fuel (rich condition)
White smoke isn't "smoke" at all...it's either raw, UNBURNED fuel vapor OR it is steam.
If you're seeing "white smoke" and it doesn't have a strong, acrid smell to it then it is likely steam or water vapor as racerone suggests.
Since the exhaust systems on marine engines, including outboards, are water cooled it's possible that this is normal under certain atmospheric conditions.
Excess steaming though could be a sign of something amiss in the exhaust piping OR a possible problem with the cylinder head.
You would think that an "overhaul" would have addressed the last two but it's possible something got overlooked like a crack in a head.
If it's not a "liveable" condition you don't have much choice but to follow up with Honda about it. You may want to ask if the cylinder heads were pressure tested during the teardown and, if so, were the results written down on the W.O.
There is a thing with cast aluminum engine components called "permeability" where the casting will come from the foundry and not be completely "solid".
When I was rebuilding automotive engines most machine shops would pressure test heads and blocks for rebuild purposes but only if requested and for an additional fee. Things may have changed quite a bit though since then.
I'm just giving you some ideas and sorry I can't be more specific but I have only seen the giant 250 but never touched one.
Good luck.
