The Phonak team has appealed to the Court of Arbitration for Sport in an attempt to win back its racing licence.
Hamilton was one of three Phonak riders who failed doping tests
Last month the International Cycling Union rejected an appeal to allow Phonak to enter the inaugural ProTour.
The ICU's licence commission was not happy with the Swiss team's behaviour after three riders failed doping tests.
But Phonak, who have now dismissed all three riders, claimed the commission had not granted them a fair hearing and have taken their case to CAS.
Oscar Camenzind was immediately dismissed by Phonak after his positive test for the banned blood booster erythropoietin (EPO) in August.
But the team initially stood by Tyler Hamilton and Santiago Perez, who both failed a newly introduced test for blood doping.
Phonak questioned the validity of the test.
Both Hamilton and Perez have protested their innocence, but Hamilton has now been dropped and Perez's contract is not being renewed by Phonak.
The UCI said last month that a new draft anti-doping policy presented by Phonak during its appeal was "a step in the right direction" but it had not been admissible as grounds for a licence application.
Phonak were also found to be in violation of UCI regulations concerning image contracts.
The UCI has granted licences to 19 teams to compete on next year's ProTour, which is due to start in January with 30 races through the year.