You didn't tell us what version of osticket your using. Since you posted this in the 0.x -1.5 (Discontinued) section of the forums my information may not be accurate for your version.
The attached screen shot is too small for me to see what you mean. I presume that you mean you want to remove the client side where it says:
Open A New Ticket
Please provide as much detail as possible so we can best assist you. To update a previously submitted ticket, please use the form to the right.
This text is located in the index.php ni the root dir of the installation.