Does New Moon Affect Stargazing After MoonSet?
For most people the Moon does not significantly impact on stargazing, even when it is full, unless they are trying to view something in a direction close to the Moon. 

For people doing astrophotography, the Moon has a bigger impact since the sky is noticeably brighter and results in fainter objects not being able to be photographed.

And for astronomical observatories, some operations are impossible at worst and severely restricted at best since the telescopes are usually larger than "home" varieties and cameras much more sensitive but most noticeably a few days either side of the full moon.

So, depending on what you are actually doing, a ~38% Moon will not be a problem and if you are looking more than about 30° away from the Moon you will not even notice it.