Gift from Someone Not Invited to Wedding

So...the title pretty much sums it up. We received a wedding gift from someone who isn’t invited to our wedding in June and I have no idea what to do about it.

For background: this girl and her husband are decently good friends with my FH’s best friend and his wife. I have hung out with this girl in a group of their friends about two to three times over the past couple years. We don’t talk outside of these situations and our only interaction is liking each others’ posts on social media. I personally consider us “friendly” but not friends, more like good aquantences. I will say they were originally on the guest list but when we decided we wanted less people (& less money to spend), I chose family members over this group of people.

Our wedding is 30 days away. FH wants to send them an invite now, which is super shady in my opinion and makes it obvious that we felt “guilty” in some way. My mom and friends have advised me to just send a thank you card and leave it at that. I will admit that I do now feel bad, but am not sad any of them won’t be at our wedding (not entirely sure if this makes me a bad person, but it is what it is I guess). FH says he doesn’t care and it’s up to me to decide.

What do y’all think? What is the best way to go about this?