Learning more about glm parameters, how to dig deeper?

I have a Poisson distributed glm where I have identified the origin parameter to be significant through comparison to a nest model dropping that parameter:

mpoi1 = glm(count ~ marker + gene, data = somedata, family = "poisson")
mpoi2 = glm(count ~ origin + marker + gene, data = somedata, family = "poisson")

anova(mpoi1, mpoi2, test = "Chisq")

Analysis of Deviance Table

Model 1: count ~ marker + gene
Model 2: count ~ origin + marker + gene
  Resid. Df Resid. Dev Df Deviance Pr(>Chi)   
1       459     349.44                        
2       458     342.11  1    7.328 0.006789 **

The parameter origin is made up of two subcategories (free and FGT). Is there a way I can identify which of the marker subcategory (duplication, proximity, phylogeny and known_target) counts are affected the most by the origin parameter?

I though a Welch Two Sample T-test might suffice but none of the subcategories returned significant. I did this by running the test on a subset of the dataset to include only one marker subcategory such as:

t.test(count ~ origin, data = known)

Despite each returning non significant, the mean was consistently higher in the FGT origin subgroup for every marker subcategory.

Please feel free to ask more questions if I have not explained myself well.