It is best to avoid having mantras or holy images on T-shirts because we lie down on them, wear them into the toilet, wash them with dirty underwear and do not regard the image as a representation of the Buddha.
Usually logos are OK, if they are lotus, jewels and dragons, etc, and not necessarily Dharma, but if, for example, the center logo contains a vajra, that is considered a tantric implement and a holy object.
If we treat the T-shirt with respect and don't lie down or wash it with other clothes, it’s OK to have a holy image on the T-shirt. This applies to the word “Buddha” as well, and it means we have to regard the T-shirt as holy Buddha. Even the signature of Lama must be treated with respect.
Dharma quotes are OK, as they make us think about Dharma (for example, the “Live with Compassion...” T-shirts). The slogan “Visualize Peace” is a passive statement—we should have more proactive statements that we want to make happen.
We can use slogans that make people think about Dharma, but there is no need to have holy images on our clothing, as the karma of disrespecting them can happen very easily and there is no need to create any more unnecessary heavy karma for ourselves. Also, we can have images of non-religious things, for example, a lotus, a smiley face etc.
There is quite a lot of difference between T-shirts and Dharma material. With Dharma material, such as posters and advertisements, it’s OK to have holy images on them as their purpose is to advertise and attract people to the teachings. Also, the material is usually in a high place, and it’s not in the toilet or on the floor. Most people who see Dharma material know how to treat it, or we can add a note at the back that explains how to correctly dispose of the material. Of course, not everyone is going to do this.