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

[roflol]

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 :}