Merc hiring is probably not an open-tender process. More like backroom personal negotiation via selected known intermediaries and representatives.
Yes, the various State intelligence agencies would definitely try to infiltrate the processes, and spend equal effort ensuring their prospective employees haven't been penetrated by other agencies. Likewise Comstar/Dragoons would be doing the same to keep such shenanigans to a minimum, for their own good name... welcome to the spy game :D
Well let's think about how this could actually work. Keep it as close to the source material as possible without having obviously exploitable holes.
Let's say I run a standard merc unit, maybe a Battlemech company that's been around for like 15 years or something. I've got a ComStar rating (I honestly don't remember exactly how the rating system works). But we'll say that that rating is a combination of a bunch of different factors, like a cross between an eBay seller's rating and a credit report. Having a history of doing mercenary work is going to get you a higher rating (and thus more job offers).
The Federated Suns is not going to take bids on their upcoming secret raid on the Draconis Combine from just anybody. "Hmm... what about this unit? 'Takashi's Ninja Dragons.' Never heard of them before, but they look pretty good. Let's see what they'll bid on this raid against New Samarkand." Nope. They're going to want somebody who has a long history of working for various Houses. So if I did some work for the Lyrans for a few years, and say the FWL after that, and then did a little pirate hunting for the Kuritans, even if I only did on "okay" job, I'll get a better merc rating than if I had exemplary service to one House for the whole time.
Part of what they're rating is your legitimacy as a merc unit. A Great House might take a small force and spin them off into a "merc unit" temporarily to try and spy on others. But they're not likely to let that unit go work for other people for 10+ years. As soon as your unit service record starts passing the normal enlistment time for a House military, your rating probably goes up. It's like when you turn 25, your car insurance gets cheaper. Let's say the Fed Suns and the FWL have a 4 year enlistment, and the Combine and Lyrans have a 5 year, and the Cappies have a 6 year. Once your unit hits that 4 year mark, your rating goes up (because it's less likely that you're a plant). At 5 it goes up again, and at 6 it goes up again. It's not proof that you aren't a spy, it's just showing that it is less likely that you are.
Backwater assignments, like pirate hunting or garrison duty on no-name planets, those jobs are probably pretty easy to get info about. Some planet that is 5 jumps deep into Combine space, they need some extra mechs for a year or two because hostilities are higher and whoever was stationed there is getting moved somewhere else. Everybody in the Inner Sphere knows that people are getting moved to the border (the Dragon is making a show of force, and
wants the Fed Suns to see). So it's not like there's a big secret to protect. You do some assignments like that for a while, or missions where you just take care of local trouble (Baron #1 hates Baron #2, and needs some muscle). Do it long enough and people think you're probably a real merc unit, and it's not actually a secret long-term scheme by a House to spy on people.
So that's the first thing they'd look at. Your "credit rating", so to speak. Anybody with a credit rating below a certain point doesn't even get to see most of the contracts available from ComStar. To even get in on the bidding process, you've got to have been around a while. If somebody has been a merc for 30 years, it's a pretty good bet that they aren't actually spies (I mean, you know, except for Wolf's Dragoons, but whoda thunk it?).