I like your improvements to the logo. I would tell them now is the perfect time to change it because it is so new. I would almost downplay the changes, so they don't feel like they're making a drastic change, which they really aren't. Try to keep it a positive experience for them - saying things like "The designer had a real good start with this, but there are some adjustments we can make which will really polish it off..." Keep it POSITIVE, and you may be able to pull it off. If they are resistant, try to find out why, and address those concerns. You also should be able to present a good rationale behind the changes you've made.
A heavy machinery rental company, whose main offerings are excavators and backhoes, has just hired me to do some design work (website and some collateral). As luck would have it, they'd recently commissioned a new corporate identity from someone else and expect me to work with it. (Before retaining my services, they'd already had business cards and some brochures made with the new logo.)
I'm having some trouble designing around the existing logo (first image below) and thought of proposing a slightly modified version (second image) to my client which I feel may be easier to work with. I would be interested in hearing what you have to say about the advisability of introducing such changes while the corporate identity is being established. Comments on whether you see any improvements that might justify the trouble are also welcome.


P.S.
- Ignore differences in colour. The first image comes from a TIFF file I was given; the second was generated with Illustrator using the colours prescribed by the previous designer.
- Please don't go into the issue of why my new client didn't just get the previous designer to do the work they've hired me for. I'm not about to turn them down and say 'go back to the other guy'.
- 'Ditch the whole thing' is not a helpful piece of advice because that's not an option.