I mean like man, c'mon, you know...
Self-extracting collets have only been around for 40 years or so but what do you expect for 30 bucks?
Rap the thing on the side with anything handy like Reg66 suggested, once you get your bit back toss it in the trash where it belongs.
Jeez, the crap people sell nowadays... Think about it: you're talking about something that'll clamp onto and hold half a pound of steel spinning at 10,000 RPM with tolerances of at least .005" TIR for balance and a decent cut. And you think you can get something like that for 23 Euros($30 US, I just checked their website)? Heck, I just paid 20 Euro(26.00 USD) for a piloted counterbore for a #10 screw...
Suggested reading: link
Granny used to tell me you gets what you pay for and it sounds like you did....
Sorry for the rant but it struck a nerve,
P.S. Welcome to the forum, lots of good info and folks here!