My advice is to claim you have completed an Integrated Course structure.
I bet half the recruiters wouldn't be able to tell you what the difference is, which schools do them or at which airfields. Given this how are they to tell by looking at your logbook and your CAA license if you followed an Integrated or Modular course?
I could tell. I could spot the slight differences in the sequence of training flights and the subtle differences in the SPIC time etc.
But unless your recruiter has been a fairly recent commercial flying instructor (they won't have been) they have no hope of spotting the difference.
Are they up to date with who are approved to conduct Integrated? At which airfields do they operate? What are their aircraft registrations? Do they stamp logbooks?
Nah. Not a chance.
It might not work if there are large gaps - 6 months or more - between your CPL and your IR. But even then I'd give you a better than evens chance of sailing through the recruitment process untroubled.
What have you got to lose? If somebody does challenge you directly tell them you thought Modular and Integrated courses means Self or Airline Sponsored. Or that the two are the same nowadays - aren't they?
Worst you will get is a polite correction and the interview will be terminated.
For gawds sake don't lie about anything else but this is something they are asking for merely out of ignorance.
Cheers
WWW