Hello Julie,
Thank you for contacting Infragistics!
I have investigated the matter for you. The functionality you would like to turn off is a standard cutting functionality of the input tag. When you drag the text from the input field and drop it somewhere you are allowed to, you are cutting it from the first place and pasted it to the other. So, you are not able to turn it off. I have created a sample in order to show you how this works with the datepicker supported by jQuery.
Do not hesitate to contact me if you need any further assistance with this matter.
Regards, Aneta Gicheva, Infragistics