Dual Graphs of T-fixed Stable Maps

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The following screenshot is taken from "Localization of Virtual Classes" paper of Graber and Pandharipande. I don't understand the following highlighted sentences. From those sentences I understand that non-contracted rational components can not have marked points, I don't understand why. Could somebody help whether I am misunderstanding? If I understand sentences correctly, why does non-contracted rational components not have marked points on them?

Dual Graph of T-Fixed Stable Maps