The 'star stamp' on the tang was a QC mark.
During the time of it's use,,EVERY Model 39 that passed final inspection off the assembly line was stamped with that Star.

It WAS NOT something of a special marking only applied to a very few of the extra special best quality rifles selected and given that mark after a careful going over.

Every M39 got that Star Marking.

What makes M39's kind of rare with that marking is the fact that Marlin only used the Star stamp QC mark for about 4 or maybe 5 yrs.

Rifles made before the use of the Star stamp and those made after it's discontinuance won't be seen with that mark of course.
But the rifles received the same inspection, QC, and care in mfg and assembly as any of those made during the short time the Star stamp was in use.

Marlin used that Star mark as a marketing point and mentioned it in their adv of that time span. A mark to look for to be assured of quality of mfg.

Why they dropped it after such a short time I don't know. But Marlin was and has always been a penny pincher of a company. Perhaps to save a 1/2cent /per rifle, it may have been the decision to do so.

There will be a very few Mod39 rifles builtduring the period that the Star marking was used that Will Not have the Star on them,,BUT these will be marked 'Second' on the frame.
They are exactly that,,second quality. Usually cosmetic in nature. Something Marlin at the time thought not worth the trouble to go back and dissassemble and re-do.
These 'Seconds' were sold to Dealers at greatly reduced prices.
The idea of selling rifles marked Second finally dawned on them that it probably wasn't a very good idea. Once the rifle left the factory it was a poor adv of their work.
So the whole idea was scraped after too long. But the rifles with that marking (and w/o any Star of course if from that era) do exist).

I don't recall the exact yrs the Star mark was in use, but it was in the mid to late 1920's IIRC.
Marlin collector sites will have it nailed down I'm sure.
They can also most likely give you the mfg date or come very close to telling you what it is by the ser#.

Those Model 39 rifles were built for use with Standard Vel ammunition.
They carried over the same bolt style as the Model 97,also built for Standard Vel ammo.
A weak web betw the lever arm slot in the bolt and the firing pin slot can and does crack with HV ammo use.

Later mfg Model 39 rifles had a modified bolt that could handle HV ammo.
The ser# on those has a 'HV' prefix;
I believe the Model 39 with the HS bolt came to be in about 1932/33.

The Model 39A always had the improved bolt, so any 39A can handle HV ammo.
A 39A bolt can be fitted w/o much trouble so HV ammo can be safely used in either a 97 or 39.
But finding a Model 39A stripped bolt for that purpose is difficult and $$.

It's just as easy to use StdVel ammo and they work and survive just fine.