Answer: Based on my experience, your instinct is right. I would remove and discard the string and the burlap (it may be synthetic, very difficult to tell them apart these days) and then loosen the roots. The clay can actually constrain the roots, especially if it is distinctly different from your native soil.
Here is more information about the modern ball and burlap plants you may find helpful. You will probably need to cut and paste the complete url into your browser to make it work correctly.
Enjoy your daphne!
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