Because your form is public, you cannot assign them back a review task from the initial instance. They must open up the public form again and submit a new instance. 

Now, there are two ways you could go about trying to pre-fill in that form for them. 

1. Use URL parameters to fill in the data

If the form only has a few fields/limited data you want to pass in, you could build the URL back to the starting form with the user's previous values in it. In your email back to the user, you include the URL back to the public form, but also include the variable values like 

PublicFormURL?variable1=value1&variable2=value2

When the user clicks on that link, it will fill in all the fields with the data they previously entered

https://www.laserfiche.com/support/webhelp/Laserfiche/10/en-US/administration/#../Subsystems/Forms/Content/populating-a-form-with-url-parameters.htm

Downsides to this solution: URLs have size limits so it only works for smaller data sets and their submission data has to be passed around out in the open, it's not very secure. 

2. Store the data in a database with a callback number

More secure and able to store much more data, you could store all of the submission data in a database. In your initial process after rejection, run a workflow to grab all the field data and store them in a database along with the instance ID of the first instance. When you send the rejection email, you can use the same method as above, but instead of sending them all the variable data, just send them the instance ID

PublicFormURL?previous_instance_ID=instance_ID

On your starting form, you'll need to add a hidden field for previous_instance_id and then a lookup to pass instance_id into your database and fill out the corresponding fields. 

This method is more secure because the submission data stays secure in the database and only filling in the hidden instance ID field with the randomly generated instance ID will pull back the data.