Can you please advise me how to remove the get (text input) parameter without deleting the input value or disabling it? Is this even possible?
Remove the name from the input.
You can put the textbox outside the form
OR
you can use Javascript and remove this specific parameter before submitting the request.
Javascript
The method Javascript will give you a lot of flexibility.
The easiest way is to switch to the POST method when submitting the form. This way the parameters are no longer passed by Url, but rather in the HTTP header that is not displayed.