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Removal of good tether from bad cap to reuse on new gas cap?

2010 Mazda5
2010 Mazda5 Touring. As title indicates, gas cap needs replacing (intermittent CEL) but the tether looks fine. OEM cap without tether is about $10 cheaper than one with tether, so if I can reuse the current tether I'd prefer that.

I do like the tether (I've lost too many gas caps in my day) so if somebody knows some way to remove the cap from the tether, that'd be swell! TIA :}