How can I delete the backups for an old Mac from my Time Machine drive?

Good morning,

I have an external hard drive that use for Time Machine backups. I previously used it to backup my MacBook, but earlier this year, I replaced this MacBook with a brand-new MacBook Pro, and have been using the same drive to backup that computer since.

The backups for my old MacBook are still on the drive though, in the /Backups.backupdb/[MacBook computer name]/ folder. I'd like to get rid of these backups as I have no use for them anymore and as they are currently taking up precious space.

I could just delete the folder, but I'm hesitant to mess with whatever Time Machine needs to do what it does. Does anyone know of a safe way to get rid of these old backups, without screwing up Time Machine?

Thanks in advance!

-Douwe