Unless of course you were provided with a Part Private Key in which case there is no chance of interference.  I have rolled a handful of vanity wallets for others using this method via @LoyceV's thread - it was for me to gain some experience at doing such things (and I always ensured LoyceV was paid as it was their thread).

If a website were to take your part private key then there wouldn't be any issue surrounding any website going rogue.