"To respect that decision" means to show understanding, acceptance, and consideration for someone's choice or decision without trying to change it or express disagreement. Full definition
I will certainly have a conversation with him, but everyone will have to respect the decision made by the club. (itv.com)
The only one who can make that call is you, taking into consideration their relationship and how well she will respect your decisions as a team. (babygaga.com)
I think you'll find that if you hold yourself responsible for the meeting being effective without your presence, people will respect your decision not to attend. (social.hays.com)