If we are not practitioners, I'd say get rid of the difficult team mate! Why should time be wasted to think of ways to give constructive feedback!.
Well, we are practitioners so here goes….
There are many reasons why people don't take constructive feedback well. Perhaps, sheer arrogance, pride, superiority complex at work. etc. What keeps us in samsara is clinging…one of the four types of clinging is clinging towards a standpoint…whatever the standpoint may be. We will continue clinging to a standpoint if we do not realize that by allowing ourselves to do this, it will only keep us where we are. There will be no progress. Therefore, this clinging must be abandoned.
People do not take feedback because they view that their standpoint is right or simply being arrogant that they do not want to be "wrong". Being right and not being wrong become their entire focus. Unenlightened beings function through the workings of the delusional mind.
So what's required to break thru to people who cling to a standpoint (which we are all as guilty off) Care for them sincerely, not just by words, but by action. I like to believe that all human beings connect and react with care and love. The constructive feedback could have been given out of care.. but has care been shown on a normal basis to build trust? Or has "care" been given only through verbal advice/constructive feedback?
In short, if we wish to be of benefit to someone, building trust and respect is important. Care and love is crucial to build the bond. Perhaps then it is the beginning to not view dealing with difficult people as "handling them" but rather benefitting them.