[Editing an logo (adobe illustrator)]

Hi all, im a new for affinity photo program. Im in a pinch right now. I was given task to make different size logo for printing purpose, so i got this logo from.my boss asking me to his request.but the problem rise when i turn the logo into high fidelity/vector ,at some part of the logo font there is a bit off from the vector effect. Now after transfer to affinity i dont know how to edit the build up ( i dont know the word in english) i will insert media frommy biss for you guys to see. Help me please to make it smooth