Hey Paul45,
Thanks for your question and welcome to the community.
Since you are replacing the existing rolled carpet with the peel and stick kind, then yes, you would need to remove the tack strips.
Depending on if you have a wood or cement based subfloor will determine how you can go about proper removal, but generally a sturdy hammer as well as a pry bar generally can do the trick. Be mindful of any remaining nails still in the subfloor from the tack strips, and remove them if they are not flush (sticking out).
Lastly, at this stage carefully inspect the subfloor to make sure it is clean and level before installing any new flooring over it, including the carpet tiles.
Joseph