I think I know what you mean OP, and I think I've experienced similar, but it doesn't bother me.
I split with my ex 10 years ago, and moved to a little village with my 3 week old baby, where I only knew one person. She was a very good and longstanding friend, but she worked full time so wasn't around as much as she would have liked to be. So basically I was on my own - no family nearby, no local friends - starting all over completely.
I went for walks in the village and chatted to random strangers, and joined all the available baby groups, and in the course of this I acquired several of what could be described as "pity friends". They were kind people, who didn't really know me at all, but saw that I had a tough life at the time, and tried to help out and involve me in things. Sometimes I wasn't invited to things because they were "couple" events (dinner parties etc) and I didn't fit, being a single parent. But it honestly didn't (and still doesn't) bother me. I don't have a dog, so I wouldn't expect to be invited on a dog walk. I don't have a partner, so I wouldn't expect to be invited to a couples dinner party.
Of course over the years I have met and made many friends, and some of the "sympathy" friends have become real friends, whilst some of them are just acquaintances who I just say hello to. But whatever their motives, I will always be hugely grateful to the people who picked me up and helped me out at a very low and lonely time in my life.
If you can, I would try and take the good from these friendships, and try not to think about anything that might be negative. And also remind yourself that they must like you, because however much pity someone can inspire, no one wants to spend time with someone they really don't like.