Twisting sideways didn’t do it for me, but sliding along the edge did. However, at first I didn’t realize that the pick was between the motherboard and midframe, rather than between midframe and back cover like it was supposed to. This led to breaking off a spring-loaded connector on the motherboard, connecting to an antenna (I guess) in the back cover. So far I haven’t noticed any reception issues, but I can’t say for sure.
In essence: be careful to get the pick towards the back cover, and not “straight in” under the midframe.