[clicks]

Small nitpick: You probably mean to say "I will apologize to your team" not "I would apologize to your team".

The word 'would' is used when expressing something in a conditional mood, often times in light of some possible future occurrence. E.g. "I would try harder if only I were getting graded for this assignment" or "I would lose my mind if anything happened to my children".

The more you know. :)