Try deadletter message on exception

TopicProcessorDeadletter.cs

[FunctionName("TopicProcessor")]
public static async Task Run(
    [ServiceBusTrigger("%topic-name%", "%subscription-name%", AccessRights.Manage, Connection = "connection")] BrokeredMessage msg,
    ILogger log)
{
    var thing = msg.GetBody<Thing>();
    var apiClient = new ApiClient();
    try {
        await apiClient.PostAsync(thing);
    }
    catch (BadRequestException) {
        await msg.DeadLetterAsync("a-reason-code", "An error description");
    }
}