Ok, what I did to realize this was adding another line with an additional extension to the affected device. Then I removed the original extension from the line group and added the newly added to it.
This way the user now has bound two extensions to his phone but this doesn't matter since the second extension is for the line group only.
Now the user is able to receive incoming calls over the pilot and is also able to use his CTI device since this doesn't collide with the line group anymore, because it's used extension isn't in the line group anymore but the newly added one.
In Detail:
Before:
Pilot: -299
Line Group: MyLineGroup
Members: -351, -345, -359 (-359 with CTI device)
Incoming call => -299 => Broadcast to Line group members => -359 doesn't react and CTI phone is not compatible with line group.
After:
Pilot: -299
Line Group: MyLineGroup
Members: -351, -345, -518 (replaces the -359 now and is bound as additional line to the device of the -359)
Incoming call => -299 => Broadcast to Line group members => -359 gets call and CTI phone works since it's extension (-359) doesn't collide with the Line group anymore.
I hope my confusing description describes the case and might be helpful to others.