Will
No pilot has any RIGHT to land on your land, whether it's an airstrip or not. Prior Permission to land must be granted by you, and you alone, for anybody to use it. If someone does land there and you do not want them to, it is your prerogative to request any size of landing fee that you so wish.
Whilst you can de-register it from any publication that it may be published in for pilot's to know about it (Pooleys/Lockyear's etc), most pilots only buy a new copy every few years so it will remain as a 'known strip' for some time to come yet. Additionally, there is every chance that its details can be found online on various websites.
The universally known "don't land here" signal for a strip is a big white cross at either end (at least 10 metres big). Or, you could just spray such a cross into the grass with Roundup.
I'd be interested to know which strip it is as this would give an indication a to how frequently you might get people wanting to use it. Feel free to PM me if you want.
Landing without permission (unless in an emergency) is blatantly rude in the flying world and if it happens, and you aren't happy about it, you have every right to be annoyed.