I'm not sure I can evaluate this without knowing what the entire essay is like. If this is an informative exposition on pet ownership, this introduction is okay, but it reads a bit like an extra body paragraph to me. It's probably not worth obsessively editing unless you are very worried about your grade, however.
The big things I look for in an introduction is the thesis statement (what point is the body paragraphs trying to prove?) and why I should care about that point that your body paragraphs are proving (the first sentence). The first sentence is like a magazine headline - the hook to get me to read.
So from this introduction, I think I'm supposed to care about this essay if I have an interest in adopting a pet. From this last sentence, I would expect to see the rest of the essay focus on an exposition of pet-sitting options and services. If that's not what your body paragraphs are truly about, I would edit the last sentence to reflect what they are truly about, and adjust the paragraph accordingly. I think your teacher may like what she sees in that regard.