Pilot Bearing pulling tool question

[basicmods]

Hello.

This weekend I am going doing a manual tranny swap, and went to the parts store to rent (loan for free) a slide hammer and pilot bearing pulling tool. However, the pilot bearing pulling tool that I have is too large to fit into the replacement pilot bushing. I know that I won't be using this with this bushing, but was checking it out as a guide to see what the difference would be with the bearing and bushing.

I guess my question is this - do i need to worry about the fact that the bearing pulling tool won't slide into the new pilot bushing or will I need a different bearing pulling tool? The only way this tool will work is if the bearing has a larger inner diameter than the bushing, which I find unlikely. Any help would be appreicated.