this is inelegant but it works

usingScreenToWorldPoint.cs

using UnityEngine;

public class Paddle : MonoBehaviour
{

    void Update()
    {
        var cameraObj = GameObject.FindWithTag("MainCamera");
        var camera = cameraObj.GetComponent(typeof(Camera)) as Camera;
        if (camera == null) return;

        var backgroundImageObj = GameObject.Find("BackgroundImage");
        var backgroundImage = backgroundImageObj.GetComponent(typeof(SpriteRenderer)) as SpriteRenderer;
        if (backgroundImage == null) return;

        var paddleObj = GameObject.Find("Paddle");
        var paddle = paddleObj.GetComponent(typeof(SpriteRenderer)) as SpriteRenderer;
        if (paddle == null) return;

        var mouseX = camera.ScreenToWorldPoint(Input.mousePosition).x;

        var leftTopOfSprite = backgroundImage.sprite.rect.min;
        var rightBottomOfSprite = backgroundImage.sprite.rect.max;

        var paddleWidth = paddle.sprite.rect.width / paddle.sprite.pixelsPerUnit;

        var xMin = camera.ScreenToWorldPoint(leftTopOfSprite).x + paddleWidth;
        var xMax = camera.ScreenToWorldPoint(rightBottomOfSprite).x - paddleWidth;

        var x = Mathf.Clamp(mouseX, xMin, xMax);

        transform.position = new Vector3(x, transform.position.y, transform.position.z);
    }
}