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Did you have a non-compete as part of your contract at all? Regardless of the letter saying you were a salesman and incorrectly describing your position, because the letter cannot change any terms of your actual contract with them. You would like to think their mistake in the letter would give you some rights, but their letter is not the contract itself, the contract is what the court would follow, not the letter they sent you as they cannot unilaterally change the actual contract you signed with a letter that clearly says it is a reminder of the contract you signed.
Also, even in Arkansas or any other right to work state, a non-compete agreement can be enforceable as long as it is reasonable in duration (not more than 2 years) and it narrowly protects the employer's interests. So they can prevent you from taking a particular job in a particular area depending on what the actual contract (not your reminder letter) states.