Best way to earn gamerscore?

Earning achievements is the only way to earn gamerscore, so play games.

The only way to have a gamerscore reset is if you have been found to have cheated/modded your gamerscore. Gamerscore resets are permanent and you can not re-earn any of the achievements you had before the reset.

If you're looking to start over, it would be best to create a new account.

If the account was given a gamerscore reset then there's no way to re-earn those achievements. The only way would be to create a new account.

Can't be done i'm afraid.

The only way to get the lost achievements/Gamerscore back would be to re earn them again.

It's always best to be connected to live if possible as your profile would be stored on the xbox servers.

That way if something happens like what has happened to you at least your Gamerscore is still saved.

As you weren't connected to live then it's all gone & there's no body that can change that for you.

There is no way have just that gamerscore removed. The enforcement team does issue gamerscore resets if you have been found to have modded/cheated to earn them and that is the only way. To have the enforcement team investigate, someone would have to file
a complaint on you via the console. They do not send you a message. If you are given a gamerscore reset, they will remove all of the achievements on your account (including the ones you earned) and you would no longer be able to re-earn any of those acheivements.