Former teacher and nanny here, I think calling a nanny weird for loving the kids she is looking after and wanting to keep in touch is odd, not the other way around.
As a nanny, some of the kids I looked after were 2 months old when I started and 2 when I left, most of them did their first steps with me and said their first words to me, I would spend 10 hours with them everyday, spending way more of their awake time with them than their parents did, not getting attached would be weird and cause for concern.
I have loved each and every of the kids I have looked after as a nanny, I am still in touch with them, I still visit some of them despite them leaving in other countries and in fact, a family I nannied for in Germany is coming to visit me this summer and I went to Berlin to see them in October.
Those kids were parts of my daily life for months/years, it would be impossible for me to leave and not look back. I would be mortified if one of the parents felt I was ''odd'' or ''weird'' for caring about their child with whom I spent most of my time with.
On the other hand, as a teacher, I have cared about my students on a different level, a more superficial one, I care about their well-being in class (and outside of class in a, want to make sure nothing that shouldn't happen is happening to them and no bullying is occurring kind of) but when I would leave the classroom, I would leave the classroom, when they would move on to another teacher/class, I wouldn't feel the same type of sadness than I have done as a nanny.
Kids are annoying, especially when you are with them for 10 hours a day and they aren't yours, to provide good care you need to love them, if you distance yourself from them as a nanny or expect your nanny to, chances you will end up with a nanny who doesn't like your kids, is counting down the hours and have little patience.
Be glad you have a nanny who cares and say no to visits if you can't be bothered but don't call her weird/odd for loving/caring about your kids.