getting rid of old caulk on kitchen sink.

[Deleted]

Our kitchen sink caulking is gross so I watched a new DIY videos on you tube and got most of the caulk up but I have two questions...

1) How do you get the caulk out of the back of the sink? There is a tiny tiny space between the sink and counter. It is nasty back there. I can see black grossness. Any suggestions on how to get back there? The space is so small I'm not sure how to fit a tool back there.

2) Now that I have gotten up most of the old caulk (except the gross stuff from question 1), there is grossness leaking out from the hole that disgusts me. Should I just pull the whole sink out and clean really well then put the sink back down and re-caulk? Or is that over kill?

Thanks!