I've recently had an email from a company
That I trained with about 4 years ago telling
Me to remove their logo from my website
And that I can no longer use their advertising
Material ( that I purchased from them). Can a company do this ?
I've recently trained with a large company who are more than happy to promote themselves through me and my salon. This "company" also wants me to remove them from my brochure. I had been told I could their logo when I had them printed .

Yes, they can. It's their copyright and they can choose whom they like to use it. If you have anything in writing that gives you permission to use it then by all means forward them a copy of it. Of course they may have changed their Ts and Cs, if for instance they've been taken over, or they've have had a change of policy.
Sorry, but themselves the rules.

A lot here will hinge on the terms of the contract stating you could use their logos and how they could be used.
If you paid for their material then there should be some sort of guidelines of what can and can't be done.
If there is no written contract then it all turns a little grey...
I would start with politely asking them why they are rescinding your permission to use their materials that you purchased from them along with the verbal agreement you had with xyz that this use would be ok.
Then await their answer...

Or you could go all guns blazing I guess But unless you have a contract or T&Cs about use of the advertising material... I'd be careful about that...

A thought occured to me whilst reading all the above - although it may be totally irrelevant -

Do you still actually still use their products and purchase supplies from them?

If they can see that you haven't bought any products for a year or two they may judge that you are using their advertising and logo to attract custom without actually using them.

Best to give them a call and ask why.