Short answer
You can delete search history by removing the conversations that contain it from the History tab, either individually or in bulk.
Full explanation
AskTuring stores your past searches as part of your conversation history. To remove them:
Open the History tab from the left-hand menu.
Check the box next to the conversation(s) you want to delete.
A menu with a Delete button will appear at the bottom of the screen.
Click Delete to permanently remove the selected conversations.
You can select multiple conversations to delete them in bulk, or use the check-all box to select every conversation in the list.