According to the information of the Supreme Court of Ukraine, the mobilization order is only a means of notifying the conscripted person for his arrival on the specified date to the territorial recruitment center. That is, it is not a decision or action of a subject of authority.
It is not possible to challenge the mobilization in court. But it is possible to challenge the conclusion of the VLK if there are sufficient reasons for this. If you want to challenge the decision of the district and city-level VLK without a court, then there is an option to appeal to the regional-level VLK for the purpose of reviewing such a conclusion. If it is necessary to revise or cancel the resolutions of subordinate VLKs, this can be done by the military medical commissions of the respective regions. And the Central VLK reviews the resolutions of the VLK at any level.