Should I be worried if grease leaks from inside the new electric drill?
It's a tool, and they use grease during assembly. The jaws of the chuck should have grease on the outer surface where they meet the collar. Spots of grease elsewhere are incidental and shouldn't be cause for concern. Those aren't necessarily assembled in "white glove" conditions.

Further, once you use it, since it has moving/spinning parts, you might see excess grease weep out in places. Again, I wouldn't be concerned as long as it operates smoothly without harsh grinding or other noises.