If you receive negative trust, then the only way for that to be removed is to appeal to the person who gave it to you. Nobody else can remove it. If you believe that you the negative trust in uncalled for, you can open a thread on Reputation to get the opinions of other forum members and to defend your case in public. This may or may not benefit your case, as other may chip in to defend either party.

Note that the linked image in the OP is a yellow trust flag, and not a trust rating. One may open a flag and not leave negative rating, or vice-versa. Flags are a newer feature, and are intended to give more visibility and warning when there is a substantial risk of losing economic assets when dealing with the flagged person, as per the criteria of the person who created that the flag and those that support it.

The idea behind it is to leave on the profile feedback and rating in accordance to what one considers to be a likely possibility of losing money or being scammed by the negatively rated person. It stands as a warning, which should be read in detail in the Feedback (some negative ratings are unsubstantial retaliation comments, which are not really the core intent of the system).

Ratings given by DTs (Default Trust) weigh more visually, since they affect the Trust counters on the profiles. Their feedback lists under Trusted Feedback. Feedback provided by non-DT (our outside your personal Trust network if you have one) does not have impact on the Trust counters, but you never know if those non-DT members may become DT one day, and thus conform part of the Trust counter values.