I imagine if they were blunt about it, they would never be employed by the ruler of those lands again.

They were plenty blunt about it, and they were employed again, and extorted from their sometime employers again.

It didn't have to be any more subtle than "pay us or else", and typically wasn't. There was no need for a pretext; the "just cause" was "it's just 'cause we're camped outside your gates with an army, and it'll go better for you to deliver us some silver, thank you very much". Deals with city states did often contain a promise by the mercenary company not to return, and the companies typically kept it. . . for a while. It's fair to say that a community could never really "buy" protection-- a deal with a mercenary company was nearly always a "rental". To the extent that the mercenary companies had any fig leaf for their extortion, a commonly heard one would be the demand for payment for some services previously rendered.

Pope Urban V described the process in 1364, and there's no hint of a "just cause":

A multitude of villains of various nations associated in arms by the greed to appropriate the fruits of labor of innocent and unarmed people, let loose to every cruelty, to extort money, methodically devastating the countryside

However, the Popes themselves were both victims of and employers of the mercenaries-- we can find plenty of occasion where they're prepared to overlook the mercenaries' past deeds, including against them, if they were of use against their enemies

[John Hawkwood's] company committed atrocities at Pont-Saint-Esprit. Pope Innocent VI condemned and excommunicated the band in January 1361 and called out a crusade against it. The enterprise failed, in part because many of the hired men, themselves mercenaries, went over the company . . . In March 1361 the pope and the company made peace. The agreement was in the form of separate accords with the various contingents that made up the company. The pontiff engaged them for service across the Pyrenees in Spain and across the Alps in Italy. [Caferro:2006]

William Caferro has examined the costs for communities to arm themselves and go to war against mercenaries -- on occasion, communities did defeat mercenary companies as for example at the Battle of Torrita, where Orsini lead the Sienese to victory over the Company of the Hat. But here's the ironic thing-- the costs of this victory weren't different than the ransom that the mercenary companies typically demanded, and the victory didn't destroy the companies' future potential. Italian city states had other choices as well-- they could band together against the mercenaries as a league, and sometimes did. But as rivals these cities often found the leagues didn't work for them.

So one can say that "the justification for the ransom demanded by the mercenaries is that in some rough way it was proportional to the avoided uncertainty (like dying) and costs of war", eg it was at least arguably an economically rational price, which is why the business minded leaders of the city states so often paid it. This makes the choices faced by the city states interesting to political scientists -- "how much do I pay to buy off a potential enemy?" and "how much is it worth to _employ_ them against my enemies? " vs "How dangerous is it?"

If that all sounds like a "Machiavellian" sort of calculation . . . it was just this world that Machiavelli was familiar with. In his Florentine Histories -- which deserve a wider audience-- Machiavelli is clear that the city states must build their own armies so as not to be at the mercy of the mercenary; he doesn't have a problem with the occasional opportunistic use of paid soldiers, but views a state that relies on them to be intrinsically weak and to serve its citizens poorly.

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Sources:

HOUSLEY, NORMAN. “THE MERCENARY COMPANIES, THE PAPACY, AND THE CRUSADES, 1356–1378.” Traditio, vol. 38, 1982, pp. 253–280.

Lynch, Christopher. “War and Foreign Affairs in Machiavelli's ‘Florentine Histories.’” The Review of Politics, vol. 74, no. 1, 2012, pp. 1–26.

William Caferro has dug deep into the relations between mercenary companies and Italian city states, see for example:

Caferro, William. “Italy and the Companies of Adventure in the Fourteenth Century.” The Historian, vol. 58, no. 4, 1996, pp. 794–810.

Caferro, William P. “Warfare and Economy in Renaissance Italy, 1350-1450.” The Journal of Interdisciplinary History, vol. 39, no. 2, 2008, pp. 167–209.

and especially his book length treatments

Mercenary Companies and the Decline of Siena, (Johns Hopkins University Press:1998) which has tables of payments to mercenary companies.

John Hawkwood: An English Mercenary in Fourteenth-Century Italy. (Johns Hopkins University Press:2006)