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.
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.