Don't even think about it.
They mean the same thing. Saying "give it a thought" drives home the point in a stronger way in my opinion. I think it's safe to say that it's somewhat more emphatic.
a thought - one thought - Don't give it a thought. Don't even devote one thought to this. It's not necessary or it's not important.
Don't think about it - It's not necessary to think about it.
Student or Learner