Compare two time strings?

So I have a timer code that counts up when starting a game. Then I convert the output of the timer to a highscore variable(string) after the game is finished. So if I start a new game, I want to check whether the new output of the timer is greater or lower than the highscore variable? Any suggestions?

Timer code:

    public Text counterText;

    public float seconds, minutes, startTime;

    // Initialization
    void Start()
    {
        counterText = GetComponent<Text>() as Text;
        startTime = Time.time;
    }

    // Update once per frame
    void Update()
    {
        minutes = (Time.time - startTime) / 60f;
        seconds = (Time.time - startTime) %  60f;
        counterText.text = string.Format("{0:00}:{1:00}", minutes, seconds);
    }

and the timer stops when it reaches the finish line(trigger)

    public GameObject successfulCanvas;
    public Text score;
    string finalScore = "None";

    private void OnTriggerEnter2D(Collider2D collision)
    {
        if (collision.CompareTag("Player"))
        {
            Time.timeScale = 0;
            successfulCanvas.SetActive(true);

            if(score.text >= finalScore) //help here

            finalScore = score.text; //ignore
        }
    }

public Text counterText;

 private float seconds, minutes, startTime;

 public float TimeElapsed
 {
      return Time.time - startTime;
 }


 // Initialization
 void Start()
 {
     counterText = GetComponent<Text>() as Text;
     startTime = Time.time;
 }

 // Update once per frame
 void Update()
 {
     minutes = TimeElapsed / 60f;
     seconds = TimeElapsed %  60f;
     counterText.text = string.Format("{0:00}:{1:00}", minutes, seconds);
 }

 public GameObject successfulCanvas;

 // Drag & drop the gameObject holding the `Time` script
 // (supposing your 1st script is called Timer)
 public Timer Timer;
 float highScore;

 private void OnTriggerEnter2D(Collider2D collision)
 {
     if (collision.CompareTag("Player"))
     {
         Time.timeScale = 0;
         successfulCanvas.SetActive(true);

         if(Timer.TimeElapsed >= highScore)
              highScore = Timer.TimeElapsed;
     }
 }

The easiest solution is to use int.Parse (or Tryparse.) to convert you score string to int again

int _score = int.Parse(score.text);