If an Embedded Data field is empty for a respondent, the email will have a blank space where it would have been piped in. Qualtrics will not eliminate the empty space for questions that were not displayed.

Because my survey is being distributed via link and therefore information is not being pulled from that link, could that be the reason why some embedded data fields are not pulling in correctly?
Also, is there a way to mitigate this?

It's hard to diagnose the issue without being able to see the Survey Flow and how the Embedded Data fields are assigned values. What kind of link is your survey being distributed by? A unique or personalized link for each respondent, or a single anonymous link that is the same for all respondents?

Is there a way to still pull data from respondents if a survey is distributed via link? I think that is where my issue lays, I am distributing through a link and not through a contact list. Therefore, data is not being collected and my piped text is not being allocated correctly.

There is a way to assign embedded data values through query strings, but that might not be applicable to your use case. Generally piping from a contact list to embedded data fields in the Survey Flow is the most common way to collect dynamic background data for respondents.