So glad that things finally got back in sync after a few days. Most interesting it took that long for things to stick. The good news about the red pin is that looks like a normal dropped pin [but named Home]. If you tap it or drag the map around so that the pin displays on the map, you will get an option to move it. Before I moved where I did, I had a custom labeled pin for my home [it was a family's home, so it was labeled as such]. In fact, it still shows up in my Favorites.
If you select that pin on the map, you will get a screen that shows many options...a row of buttons - drive time to that pin, whether the place is in your offline map, move, and a More ... button. Below that are details about the pin - the address, GPS coordinates, and then a section about reporting something wrong, adding/removing from favorites and simply remove, in red lettering. Both that remove link, plus in the More... button - it has a Remove link too. Tapping on either one of those will finally get rid of the red pin labeled Home.
You can also long tap the red pin in the map view, and a pop up menu appears that has a "remove pin" option.
That said, that's the default behavior for a Dropped Pin. I was unable to rename that pin, so I went to my current location to see if I could remove the custom labeled pin named after the family house. It has a different pop up menu when I long tap it, and single tapping it, gives me less options as well. It is both in my favorites and in a Guide. I have the option to remove from my favorites. I did that, and I removed it from the Guide it was in. But it remains.
The icon itself on the map has a star, but I did remove it from my favorites which uses the star icon. I wonder if this will take a bit to actually remove.
Hah! And somehow that magically removed my blue Home! Which is something I want to keep [I like to be able to say to Siri, "navigate me home" and boom she starts turn by turn back to my house].
For me, I have a frustrating problem with Maps in that something in the database that powers Maps on iPhone is corrupt, causing my entire Maps database not to sync to my Mac. It's been like this for 2 years, and multiple iOS/macOS upgrades. I have a lot of favorites/Guides so I've been manually moving things around on my phone, but trying to build an example for you, I may have found the corruption!
The location still shows up in my Favorites even though I removed it from there. So I am going to take a semi educated guess and say that if you remove your red pined Home from your favorites [if there is no option to simply remove it completely], then wait a few days, it may revert to a normal named Dropped Pin, which you can long press and remove, or single tap and see the option to remove. I do not understand why a lag is there when having Maps.
I was able to put my blue Home back into Favorites just now - went to my My Card in my contacts, tapped the home address, and then the More ... button to add to favorites and now it shows as the first icon in Favorites. The old family named pin still shows up though. I wish I understood why in your case it took a few days for the change to apply. I am going to do the same here and see if my custom labeled red pin leaves since I did remove it from Favorites.
It's also 5am and I woke an hour ago, so my brain may not be firing on all 8 cylinders right now.
I guess the exec summary is - find that red pin, long tap and remove it if you can. It probably is in the favorites, so tapping it and removing it from Favorites is your first step to getting rid of it. It may take a day or more for it to leave your favorites - at that point, it will hopefully revert to a non custom name of Dropped Pin, which you can then just tap on, and use the remove feature
I'm willing to bet your Maps database has some corruption too. For me, I know this due to Console on my Mac reporting corruption in the SQLite Maps database every few seconds.
