Design pattern for dynamic C# object

I have a queue that processes objects in a while loop. They are added asynchronously somewhere.. like this:

myqueue.pushback(String value);

And they are processed like this:

while(true)
{
    String path =  queue.pop();
    if(process(path))
    {
        Console.WriteLine("Good!");
    }
    else
    {
        queue.pushback(path);
    }
}

Now, the thing is that I'd like to modify this to support a TTL-like (time to live) flag, so the file path would be added o more than n times.

How could I do this, while keeping the bool process(String path) function signature? I don't want to modify that.

I thought about holding a map, or a list that counts how many times the process function returned false for a path and drop the path from the list at the n-th return of false. I wonder how can this be done more dynamically, and preferably I'd like the TTL to automatically decrement itself at each new addition to the process. I hope I am not talking trash. Maybe using something like this

class JobData
{
   public string path;
   public short ttl;

   public  static implicit operator String(JobData jobData) {jobData.ttl--; return jobData.path;}
}