Fiancé's dad inviting more guests-help!

To start off, my FH is not close with his dad at all ( or his fathers side of the family) and is more or less including him out of respect, since it’s still his dad after all.
This weekend his father sent a text to us saying “Hey give me a call when you can, I have a few more people you need to invite”, followed by the list of people, and their addresses. This didnt sit with us well seeing as we have already sent out save the dates, and Had gone through the guest list multiple times with his dad to ensure that was everyone.
His dad said he would pay for the extra guests but we don’t want that for 2 reasons: 1. We don’t want to take any of his money, as he is the type of person to hold it over our heads and we don’t want to give him any control over the wedding. 2. Yes, the extra guests would run up our expenses, but it really wasn’t about the money to us. We feel if these guests were so important, then they should’ve been on the original guest list. My FH has met some of these guests maybe once or twice when he was a kid, but other than that , has no current relationship with them; the others he has absolutely no idea who they are.
We’ve also come to learn that his dad has already verbally invited them to our wedding without speaking to us and is saying “well they probably won’t come, just send an invite and then they will send you a wedding gift.”I was always told that even if you thought that a guest wouldn’t show, you still had to intend for them to, and I don’t like the thought of sending out invites just to get a gift. We have been more than accommodating when it comes to who our parents want to invite as far as distant relatives and a few family friends, but it really bothers us that these people weren’t originally on the guest list so we don’t feel like they need to be invited.
I told my FH it was more or less his call on what to do, since it was his side of the family and I didn’t want to cross any boundaries, but his dad has started messaging me separately saying that “it’s no big deal, just send a couple more invites in the mail.” And that “I’m sure you invited whoever you wanted, why can’t I” ( It’s not “a couple” invites, it’s 10 people, and a few plus ones, and I have cut down my side of the guest list a considerable amount already to fit with our budget and who we actually want at our wedding.)

Neither of us are sure what to do! Has anyone else dealt with their parents inviting people like this ??? How did you go about it ?