How to add embedded data to a survey invite on email distribution

Hi,
I'd like to schedule a survey with 4 iterations, and each iteration runs after 3 weeks.
I want an embedded data field "iteration" that contains the number, so 1, 2, 3 or 4.
The easiest way to me seemed to include this number into the survey url on the scheduled distributions (so distribution scheduled on today has iteration=1 and the distribution scheduled within 3 weeks has iteration=2).
However I can't find how to append embedded data to the standard survey link field:

${l://SurveyLink?d=Take the Survey}

I tried
${l://SurveyLink?iteration=1&d=Take the Survey}
${l://SurveyLink?d=Take the Survey}&iteration=1
${l://SurveyLink?d=Take the Survey&iteration=1}

None of these combinations seem to append to the actual url.
It does work with the url field that doesn't have a description:
Or copy and paste the URL below into your internet browser:
${l://SurveyURL}&iteration=1
but I do want the url to have a text description instead of the long url...
I also don't want to hardcode my survey url as I want to reuse this message as template, and I'm using individual links.

Anyone an idea?