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It's not gibberish, it's an Id, which is the type of data Salesforce stores for all Lookup or Master Detail relationships. If you want a linked name, you will need something more like the below. I would change the var to assignment to be less confusing.

<apex:pageBlockTable value="{!team}" var="assignment">
    <apex:column headerValue="{!$ObjectType.User.fields.Name.label}">
        <apex:outputLink value="{!$Action.User.View, assignment.Team_Member__c}">
            {!assignment.Team_Member__r.Name}
        </apex:outputLink>
    <apex:column>
</apex:pageBlockTable>

SOQL:

SELECT Team_Member__c, Team_Member__r.Name FROM Team_Assignment