Balogun was sent off by Claus after a VAR check in the last-32 win over Bosnia and Herzegovina for planting his boot into the ankle of Tarik Muharemovic.
However, FIFA later suspended Balogun's red-card ban. Trump said he had asked for the decision to be reviewed, describing Claus as "a little bit suspect if you check his past" without elaborating.
"FIFA recognises Raphael Claus as one of the world's leading professional referees and a valued member of Team One (FIFA's elite group of referees) at the FIFA World Cup," FIFA said in a statement.
"Throughout his career, he has consistently demonstrated the highest standards of professionalism and integrity."
FIFA said Claus was not available for comment, in line with its policy of referees not speaking to the media during the tournament. FIFA President Gianni Infantino said referees must be respected.
"Once more, I reiterate that we must respect the referees and respect the rules that govern our game," he said.
"It is very simple and cannot ever be overstated - without referees, there is no football."
Claus has officiated in over 600 matches in his career, and Pierluigi Collina, FIFA's Chief Refereeing Officer and Chairman of the Referees Committee, emphasised the organisation's faith in the 46-year-old.
"Raphael Claus is refereeing at his second FIFA World Cup having been with us in Qatar in 2022," Collina said.
"He is an experienced and highly respected referee and we maintain full confidence in him as a trusted match official."
Balogun was eventually allowed to start Monday's last-16 clash with Belgium and was named in the starting lineup by coach Mauricio Pochettino.