There are several places that may cause a leak on that pump, and I suspect its meant to do so...
First you have to remove the clutch cover, when that is done you have it right in front of you.
It looks something like this, I never had an OEM 038/380 pump but I have several aftermarkets ones and they are all a little different, but basically of course they are all a copy of the one you have.
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These are the basic main parts; piston, adjuster shaft, a rubber plug that seals the end, and the drive gears.
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That rubber plug is capable of popping out if it is not installed perfectly dry, that would cause a massive failure.
The most obvious seals are the main gasket between the pump and the crankcase, and the rubber seal ring that seals the gear shaft. They are in my experience the least probable cause for a leak, but of course on an old saw that rubber seal might be worn and fail.
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If you have a new pump and a new pump gasket then you don't have to worry about that.
One place it may leak is at the ends of the adjuster shaft, there should be some rubber o-rings there;
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Again if you have a new OEM pump you probably don't have to worry about that.
Now look at these gear shafts;
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You see they are open in the center where the axle for the gear shaft comes through - so that the bar oil can seep through there and lubricate the axle, after that the bar oil will seep out to the circular hole in the plastic gear and get thrown outwards on to the gears and perhaps help cooling the clutch bell as well so that the plastic gear on the cluch bell doesnt melt.
As long as there is oil in the tank there will always seep oil out through that axle, and it will accumulate inside the clutch compartment and finally on your bench top. Now the OEM pump might have such a super perfectly accurate fit and tolerance so that the oil leak will be minimal, but it will likely be there.
On the aftermarket pumps the tolarance between the axle and gear-shaft is not usually that great, and in worst cases it might pump more oil in to the cluch compartment than to the guide bar and chain.
I simply glue a patch of rubber gasket sheet with CA glue over the axle hole in the plastic gear and my copycat saw don't leave any oil on the bench. With an OEM pump I would try it as it is first though.