2 Corinthians 7:10 For godly grief produces a repentance that leads to salvation without regret, whereas worldly grief produces death.

It would seem from this verse that the source of grief is more important than the repentance itself. 

International Standard Bible Encyclopaedia

Repentance:

re-pen’-tans:

I. OLD TESTAMENT TERMS

1. To Repent-“to Pant,” “to Sigh”

2. To Repent-“to Turn” or “Return”

II. NEW TESTAMENT TERMS

1. Repent-“to Care,” “Be Concerned”

2. Repent-“to Change the Mind”

3. Repent-“to Turn Over,” “to Turn Upon,” “to Turn Unto”

III. THE PSYCHOLOGICAL ELEMENTS

1. The Intellectual Element

2. The Emotional Element

3. The Volitional Element

How can we simplify something that our educators have made so complicated?

How can we believe we have grieved God if we do not believe there is a God that cares about each of us as individuals?

Can someone who does not believe there is a God repent?

Perhaps but the purpose behind repentance is salvation and without God there is no salvation.