the only way I have ever been able to remove caulking is to take a razor blade to both up and below the caulking line and scrape it out, should be able to pull it out like a long string, good luck and charge accordingly
ps also an old wallpaper trick is to unplug the end of the caulking tube and empty the contents, tint and mix to the color you are using. replace back into caulking tube replace plug. obviously if using latex stain use latex caulk and oil stain use oil based caulk.