Wrong profile picture is shown in mails

I have an issue with my mail. Recently I noticed that the icon shown to someone on Gmail who I've sent an email to is a super old profile picture which I think I've used on Gmail a long long time ago. The picture is no longer on my Google profile and has never been used on my iCloud account. However, when I send an email from my iCloud account to an Outlook email there is just my initials as profile picture, which is what I want.

I've looked at other posts but none has solved my issue. Some have mentioned Google Contacts but the profile picture I have on my Gmail account isn't the one shown while sending from my iCloud. Like I said, the picture shown isn't used anymore and isn't posted anywhere either so I don't understand why THAT picture shows up.

How come there's an issue with Gmail but not with other platforms and how do I get rid of that old picture? It's from when I was young and my email with @icloud.com is the one I use at work etc. so you might understand why I want just my initials when sending to a Gmail account as well.