Incompatibility problem with Word - anyone spot anything obvious?

[MrsSteptoe]

Client sent me a document shell which is a 97-2003 file (yup, I know).
I saved it down without changing the file type onto a Windows 7, Word 2010 laptop, processed the work, returned it (saving the shell document, in which I'd pasted content, under a different name), all good.
The next day, I repeated the exact same process using a Windows 10, Word 2016 laptop, processed the work, returned it, and the client couldn't open the files.
On both laptops, I only ever saved files as 97-2003 files. The files prepared on my newer laptop still said [Compatibility Mode] at the top of the screen.

My question is: how can I return openable 97-2003 files to my client from my newer laptop? Anything obvious occurring to anyone?
I'm reluctant to go back to the client with any questions about their systems and would rather try to solve it at this end.
TIA, for reading if nothing else!

What is the document like - is it just plain text or is there tables, bullets, formatting etc?

Plenty of formatting - all set up using styles, and I've allocated keyboard shortcuts to the styles I use. There's also one simple macro for pasting unformatted text. No column layouts, no section breaks, one logo. (I'll check how it's inserted - sometimes anything other than In Line With Text causes problems, though not usually compatibility problems...)

Right, logo is in line with text, sitting in the doc header, page setup is set to different first page. I don't think that's it.

save as RTF (format)?

That's a great thought. I'll give it a go. My plan is to keep trying different solutions, because DH's laptop is on its last legs. One more hot cross bun laden with jam lands on its keyboard, and I reckon it'll turn up its toes.