Often worth examining the words and numerical result together.
"Did not support..."
"not...having a substantial effect on transmission"
This was the numerical finding:
"In pooled analysis, we found no significant reduction in influenza transmission with the use of face masks (RR 0.78, 95% CI 0.51–1.20; I2 = 30%, p = 0.25)"
The RR is the risk ratio with the masks; a value of 1 meaning there was no difference in transmission. So 0.78 means there was a 22% reduction.
The "95% CI" is a confidence interval for the entity of interest, which although found to be 0.78, could have been anywhere in the range 0.51 to 1.20, though more likely closer to 0.78 than further away.
The p value of 0.25 represents a 25% chance of such a difference arising by chance. For statistical significance it is normal to look for p less than 0.05 (hence the '95%' confidence).
There is another sign that the result was not considered statistically significant. For a p value to be exactly 0.05, the CI would have had 1 as an endpoint, eg [0.3-1.00]. p less than 0.05 corresponds to a CI where 1 is outside the interval, which is another way of expressing the change in the risk from 1, and the interval taking account of the uncertainty. In other words, if 1 is outside the interval, then we can be 95% confident that the value of interest (the rate of transmission), has changed from the intervention (mask-wearing).
The requirement for p to be less than 0.05 represents quite a high bar and may result in what is still evidence of a an effect being rejected as being not statistically significant, even though it might be medically significant. This study included over 10,000 patients, noted a 22% reduction but that was not enough to give statistical significance. Yet based on this data, a 22% reduction would be the most likely true figure. A 22% reduction, if genuine, would be significant benefit. It might take that reproduction number below 1 for example.
What stops the result being statistically significant is that the number of participants was too small for an effect of this size to be 'that unlikely' due to chance (I presume some of those 10,000 were only included in other measures like hand washing but not masks). Had the study been larger and reported 22% reduction, it could have been statistically significant.
It is quite likely based on the data that the true reduction is around 22%. It could be stronger (cf that lower value of 0.51 in the CI, a reduction of half), or it could be weaker or even non-existent (because the upper range of the CI includes 1).
When the CDC says
"Evidence from RCTs of hand hygiene or face masks did not support a substantial effect on transmission of laboratory-confirmed influenza"
it raises the question of what IS substantial. They were talking about flu, but Covid-19 is a more dangerous pandemic.
If the true reduction is indeed around 22% or higher than that fully justifies wearing a mask. It just means that there are other measures that need to be identified and taken for the virus to be eliminated.