One way to study the problem would be some kind of GLM. For example, a Poisson or negative binomial regression with an intercept term and the $\{0,1\}$ variable for age is an obvious starting point. This model doesn't make any assumptions about how the age indicator variable is distributed, so it doesn't matter if it's heavily skewed in favor of younger or older workers. The coefficient estimate will tell you the direction and magnitude of age on the number of endorsements *even if* there's a disparity in workers' ages.

Here's a demonstration using some fake data generated according to the process you describe. (The code is for R.) The data generation process fixes our parameter of interest $0.15$, and the intercept at $0.5$; this is the vector `beta`.  Then we generate a binary indicator for the age variable that is $1$ only about 80% of the time; including an intercept, we have `X`. Then we generate the outcome `y` (endorsements) conditional on the expected value `lambda`.

    set.seed(1969)
    n	<- 2000
    beta	<- c(0.5, .15)
    X	<- cbind(rep(1, n), rbinom(n, size=1, prob=0.2))
    lambda	<- exp(X%*%beta)
    y	<- rpois(n, lambda=lambda)
    summary(glm(y~0+X, family="poisson"(link=log)))
    >    Estimate Std. Error z value Pr(>|z|)    
    X1  0.49279    0.01954  25.219  < 2e-16 ***
    X2  0.17504    0.04079   4.291 1.78e-05 ***

As we can see, the model estimates the effect of age at roughly $0.17$, which is within 1 standard error of its true value, $0.15$.

But this doesn't necessarily mean that the study was done correctly. In my example, we precisely know the form of the data generating process, so it's very easy for us to re-create it. If there are other features influencing endorsements, then the authors' model suffers from omitted variable bias, and the coefficient estimates will be biased and inconsistent.

I suspect this regression, or some related variant, is what the researchers used. But this doesn't necessarily mean that the effect is as large as they stated (if it exists at all!). Perhaps the researchers selected the $35$ year age cut-off after examining the data, or any other kind of bias in the model construction step created the result ("The Garden of Forking Paths").

More subtly, it's possible that the trend is not binary at all but rather varies continuously and non-monotonically over one's life and is interactive with other worker characteristics. For example, it's possible that, as a function of age, there is some complex relationship as below. In this case, the estimates from the binary model will still be perfectly valid, but will not characterize well the kind of variation actually exists. A more flexible model, such as with splines, would be able to capture this.
![enter image description here][1]


  [1]: https://i.sstatic.net/uD2L1.png