Teachers are usually paid on a union scale. No guesswork needed. What did the other teachers do that made them worth $10k more than this lady?
The men probably did nothing to warrant the extra $10,000.
Just a guess, but the story does say that the school district's policy is to pay new hires five percent more than they were making in their old jobs. If that's the factor in play, it suggests that the men were older and more experienced. Or perhaps they were lateral job switchers moving into teaching from careers in other fields where they were being paid more.
Issues like this can get very tricky very fast. I benefitted from this once, a couple of previous lives ago. It was a job I really wanted so I would have taken it anyhow, but the employer's policy was that they wanted people to show up on day one with a happy face. A salary bump from one's previous job was one way of institutionalizing this. I did not turn it down.
Prohibiting this kind of practice would have the effect of inhibiting lateral transfers and job switching, which always involves a risk. (This is one of the hard-to-measure attitudinal differences that probably contributes to male-female salary differentials. Men take more risks, as evidenced by the fact that men incur over 90 percent of workplace fatalities. They are also more aggressive in chasing pay, which sometimes works out and sometimes doesn't. Been there, done that, both ways.) It would also crimp recruitment to fill critical needs. In my case, I was being hired to fill a hole that had become a real problem for the office. The people trying to cover that particular niche as a collateral duty were drowning in it, and it wasn't their forte even had they had time. When what you really need is a Sphinx, only a Sphinx will do.
Another consideration: if one really, really, really wanted to level male-female pay differentials, one remedy would be to eliminate seniority increases. Women on average will miss years of service to stay home with young kids. If they do, they will always be behind the men in seniority-weighted pay systems. If there is a salary range for a given job, people will eventually max out, but this may take many years. It is common to find offices with a cadre of lifers who are at the top of the range working with more junior employees, younger and often female reentrants, who are doing the same job for significantly less pay. So: should we get rid of seniority pay, starting with step increases in federal service?
People on the left reflexively drift towards the demand that pay be regulated along the lines now common in government service. Bureaucrats like to base pay on objectively measurable factors like academic degrees, number of people supervised, and skill sets as enumerated in job descriptions, the KSA forms in the federal service, and on resumes. The result is rampant resume padding, out of control credentialism, and truly amazing -- really, you have to see it to believe it -- grade inflation in position descriptions. This surfaces from time to time when a competent outside auditor seriously evaluates federal vs. private sector position descriptions based on a thorough desk study of the work actually performed. It is very common to find federal positions rated as "senior" when the same tasks in the private sector are being done by junior and mid-level people. But because OPM accepts agency job descriptions at face value, many federal positions are seriously over-graded in terms of GS level.
The alternative is to allow employers to pay what they need to pay to meet the needs they perceive at any given moment, and to evaluate people based on performance. But that requires taking responsibility. It's not what bureaucracies do well.
For this sad state of affairs, I fault Congress, not federal employees. The latter are trapped in a dysfunctional system and are simply playing the system by the rules that exist. In general, federal pay scales are severely compressed. The feds pay very, very well at entry level through middle management. Senior managers are underpaid. Many do indeed leave; there is more movement in and out than many people realize. Those who do stay are attracted by the unparalleled job security and the attractive pension. But I will say this: you would be hard-pressed in the private sector to find someone running a five billion dollar a year operation and earning $170,000 a year. Or serving as SFO or chief legal counsel of said operation, for a like salary. And many of those federal lifers are very, very good at their jobs. At the branch chief and administrator levels, you are dealing with people who have been competitively selected for promotion for 30 years. A few are just time servers, but many of them are very sharp cookies who know their agencies, programs and the underlying law and regulation in infinite detail. These are the people the pay system needs to find a way to keep.