Throw a party!
So, you can block the telepath form reading with tinfoil hats. On the other hand, both a group mysteriously in tinfoil hats, and a group who mysteriously cannot be read, will be highly suspicious if approaching the guards or the telepath. The guards may notice group, the telepath might look to see their intentions (and see, not just a "lack of negative" but a lack of anything), and if the group cold overcome the guards and telepath while on full alert, they wouldn't need the tinfoil advantage! And getting caught will expose the plot, the tinfoil advantage, and the group.
So... buy up stocks of tinfoil - lots and lots and lots, please. Pick up some spray-paint, some paper, and, critically, glitter. And throw a party!
The point is, make lots of tinfoil hats. Make paper hats. Make mixed hats. Make tinfoil not-hat acessories, clothing accessories, and other decorations, and also craft with paper ones, add paint and glitter and decorations liberally. This crafting step can take as long as you need. Openly tell people you want to plan a party or parade, in honor of whatever holiday or event is closest to your chosen time. Make sure your group knows you've got something planned for the day after the party. Those of your group in the know, must wear a thin layer of tinfoil under regular caps, and only take them off if they're very sure they won't give anything away (like timing, date, or tinfoil advantage).
And, on the chosen day, have your group wear their souped-up, decorated, shiny tinfoil hats. Let them hand out hats (tinfoil, paper, mixed) to anyone and everyone. Drape passers-by with tinfoil decorated scarves, belts, toys, necklaces (made of paper, of course, to be cheap). Hand out sugar, sprinkle confetti, and basically get people laughing, worked up, joyful and a bit reckless. Make sure the wine and beer flow liberally (seed the crowds with people willing to share their flasks). Get everyone hyper.
Everyone, everyone is suddenly wearing tinfoil hats. Your group wearing them (and other decorations) will not stand out. People are up and active and excited, making them harder to read - and masking that chunks of the population will be wafting in and out of readability as hats get passed around, donned, swapped out with paper ones, or forgotten. your group being mostly-unreadable will not stand out. Now is the time to act! (please remember to let your group know that, it's not tomorrow after all! It is happening today!)
Grab some young and reckless teens (not known for sound decision making), Maybe a few of the party-reckless adults, and prime them with the idea that, poor telepaths, the local one (or couple) should be included in the fun. Include as many as you can in your group, and approach the telepath's location. The guards will see the tinfoil, but so many people are wearing them. The telepath will notice some are invisible to their senses, but those who are visible - are harmless, looking to invite the kid to party with them, have fun, cheer them up! They are handing out the decorated hats and drapes! (oh-is-that-why-people-are-hard-to-read, the telepath goes) The telepath will probably, sheltered kid, think them harmless - maybeso even let them in. Certainly not let the guards overreact to harmless kids, fuelled with sugar and alcohol!
And, yeah, once each group is close enough, and once the guards have been told they aren't a threat, once the telepath is within reasonable reach - your group surges forward, with a shout of good natured cheer, and proceeds to an old fashioned assasination. If they managed to get close enough, the atmosphere wild enough, the camouflaged people thick enough - they might seem to have simply tried to sweep the telepath up in their celebration, and some dastardly rogue assassin took advantage (instead of the whole group being in on it).
If the group has enough people, assassinating several telepaths at the same time in different locations might get really good results. The remaining telepaths will be reeling, and the overlapping coverage will be in tatters. There will once again be zones uncovered, there will be unrest, a scandal of how telepaths managed to be surprised like that. The gurads will be crippled - c'mon, how much will they have leaned on the telepaths for answers of where to go and what to do, instead of investigating, planning, and acting on their own?
The group can openly beat their chests and voice outrage about the monsters who have defiled their innocent festival, and launch their own investigation that (accidentally) completely muddies the waters. They can question, or have "clean" allies question, just how effective the telepath setup could be if they didn't see the "rouge assassins" plotting, or even striking, just because of a holiday! Some can carefully use this proof-they-are-not-omniscient as an excuse to bring up questions about how certain they are, that the kids were that sensitive, that accurate, that they hadn't made other mistakes in the past, let the guilty go, or pinned crimes on a nearby innocent. As an extra bonus, they may drum up enough doubt to discontinue the telepath program or even set the telepaths against the government! After all, the surviving telepaths will not be pleased to suddenly be questioned on their certainty and reliability after their group had already been attacked!
As a side note, if tinfoil hats are really, really rare in your world, or if your people aren't quite so likely to get caught up in a society-wide party, a slightly more staid alternative would be to periodically hand out hats to groups of teens and kids, sell them at other times, and basically take a long route to making them a passing fad. Once they're not-unheard-of, spreading hats to a smaller population segment (teens and kids will always leap at shiny things), or hosting a smaller party might still work to yield the "cover people" for the telepath to read (made up of reckless teens who mean no harm) to get the groups close enough for an assassination.