Without accepting any potential liabilities to liquidate damages and underlining the owner does this on his own risk: I was scared, but I hammered the bushing out with a socket from the other side (quite gently, it went out). I think I put some grease on it before. The clip just expands, there is space there for this expansion in the bracket. Then I pressed the new one in on the vice gently, having warmed up the bracket with hot air blower (because I was very scared, not being sure if it made sense).
If you want to take this clip out, you just need to pry it out with a screwdriver by inserting the screwdriver between the ends of the clip... I am not sure, but I think I did it on the other bracket.