Your best bet would be less of removing it, and more of hiding it.
You can edit /include/open.inc.php to remove the Help Topic label and turn the dropdown into a hidden form field that has a default value in it.
The osTicket system itself, categorizes and tracks tickets partially based on the Help Topic value.
Would Need to find: (Line 56 - 74)
<tr>
<td class="required">Help Topic:</td>
<td>
<select id="topicId" name="topicId">
<option value="" selected="selected">— Select a Help Topic —</option>
<?php
if($topics=Topic:()) {
foreach($topics as $id =>$name) {
echo sprintf('<option value="%d" %s>%s</option>',
$id, ($info==$id)?'selected="selected"':'', $name);
}
} else { ?>
<option value="0" >General Inquiry</option>
<?php
} ?>
</select>
<font class="error">* <?php echo $errors; ?></font>
</td>
</tr>
And replace with:
<tr>
<td class="required"> </td>
<td>
<input type="hidden" id="topicId" name="topicId" value="<STRONG><s>**</s><EM><s>_</s>topic_id from your table<e>_</e></EM><e>**</e></STRONG>">
</td>
</tr>
That should eliminate the field from your form while still passing a value for the ticket system to use.