I think I must be missing something. If you'll be at work for 7 hours, how will LO be fed then? Why can't they do that, whatever it is? Or will you be able to take LO to work?
That aside, I'd simply ignore it if they're just being awkward about nursing. Just keep stating what you're doing and why it's not possible for them to look after LO and don't be drawn into a discussion about it. How you feed your baby is about your baby and you, nobody else. If, in their eyes, their selfish desire to babysit trumps your baby's need for proper nutrition they're probably not the kind of people you'd want looking after your child anyway.
It may also help to remove breastfeeding from the 'problem' altogether. I don't ever leave my kids with the in-laws and they're 4 and 2 years old. I just don't feel okay about leaving the kids with them. When my oldest was a baby, we just said I wasn't ready to leave her and after a while it was forgotten, when it became clear that I wasn't going to change my mind with repeated asking. If they asked now, I'd just say something like, "Oh great, thanks for the offer. If I ever need you to babysit, I'll give you a call". Saying something like that kind of puts people on the back foot as it makes it clear that you view babysitting as something kind they're offering to do to benefit you and the baby, rather than it being about what they want (which it is, but they probably won't want to shout out about!).