The iGrid.TextBox object property of the iGTextBox type represents the default cell text editor. Its Text property is used to retrieve the current text entered by the user, so what you need is iGrid.TextBox.Text.
From the other point of view, if we understand your task properly, you are implementing the classic auto-complete text editing. Maybe, you have some specific requirements, but the built-in iGrid drop-down lists can be also used for that. Look at the 'Cell Text Auto-Complete' sample in the main demo.