That’s not really a trick. It’s how contract law has worked for years.

Of course, doing it without telling the new employer is a great way to get an offer rescinded.

Also, if you modify it after the other side signed, then you’ll want them to initial the changes.

If you modified it, then they signed without noticing the modifications, then I guess ask a lawyer.

I don’t see what outsourcing has to do with it. If they have power of attorney to an external HR firm, that seems like their problem. (I’ve never encountered a company dumb enough to do that though.)

Since it would be difficult to prove when changes/strike-outs occured relative to signatures, any such changes to the pre-printed agreement should be initialed by all parties.