Lambda triggered by SQS queue : How to manage errors correctly

We are building a conversation engine that could sometimes encounter rate limit when calling an external API. We are currently struggling with the fact that AWS reduce the concurrent run of our lambdas connected to our SQS queues when theses lambdas are failing, because when we encounter a rate limit error, we throw the error for the lambda to fail and wait for the retrying process of the SQS queue.

We searched a way to release gracefully messages in the queue without triggering an error. We found that we could set the visibility timeout of the current processed message to 0, but it seems that the sqs polling system of lambda is deleting the message at the end of the run of our lambda.

Do you have a workaround to enable us to gracefully manage errors in our lambdas and release the message in the queue ?

Thanks !