I owe a credit card $700. I want to pay the full amount. they have turned it to a Collection agency.

If you are able to pay the full balance owed on your credit card (including interest and any penalties), you should send the check to the credit card company, just like you send in your normal payment, with the payment slip included in your bill.  Write "Payment in Full" in the memo line of the check.  If the credit card company cashes the check, your bill is paid in full and you can use this information to tell the collection agency not to contact you again.

The fact that the credit card company turned the account over to a collection agency means you were in default of your agreement with them. Since the credit card company does not own the account anymore, they cannot take your money since they do not have any account to apply the money to. You can always refuse to pay but you are incorrect that you "don't owe them a dime;" and there will be consequences if you refuse to pay. The reality is that you entered into an agreement that allows whoever lent you money/gave you credit to transfer the debt to another person along with all the rights and liabilities associated with that contract; which they did in this case so now you owe the collection agency.