I say better to create a MH model with clothes in generic textures then edit.
Yes, you can edit the source files within MakeHuman but doing that could make it more complicated the next time you want a model with customized clothes, such as a T-shirt. You, likely, only want one version of those customized clothes for the model you are working on. Next time, you'll probably want something different. Better to have each model customized the way you need it, at the time, then to have a dozen one-off customizations clogging up your installation of MakeHuman.
To that end:
Create your model within MakeHuman then export it to Blender but make a special folder just for that character, first. Make sure the "textures" folder is in there with the copy of your character's .blend file.
Create a new material for your custom T-shirt or modify an existing one until you have something like this...
In this diagram, the GREEN box is your original Texture/Normal Map which simulates the folds, wrinkles and seams, etc. This will likely be unmodified from your original material. The RED box is your "new" diffuse image which creates the colors, designs or logos that will appear on the T-Shirt. This is the file that you will want to modify with your new logo. (Or create a new file from scratch.)
Use Photoshop, GIMP or whatever application program you want to make the new diffuse image file and save it under a new name. ("T-shirt_2.png" for instance.)
If you have done your job correctly, your new, custom texture design should appear on your character's shirt. Sometimes, you might have to go back and tweak your edits and/or adjust the object's UV map to get things lined up right.
Alternately, you could do something like this...
In this case, the BLUE box is the original diffuse texture for the clothing item, UNMODIFIED. The RED box is for the new logo you want to superimpose upon the clothing item. This file will be created with whatever graphics software you use (PS, GIMP) but be sure it's saved WITH TRANSPARENCY. (GIF or PNG... JPEG won't work.)
If you notice, there is a mix node. Also, notice that the ALPHA output of your logo file is connected to the FAC input of the mix node. This will cause your logo to be superimposed over top of the original texture. Of course, you'll have to make sure to tweak your UV map in order to position the logo where you want.
This would be the better choice if, for instance, you wanted to outfit a football team with uniforms. You could put the team design in the blue box and only the player's name/number in the red file.