I seriously doubt that you can purchase an ICE ticket from Strasbourg to the border or from Strasbourg to Kehl from either SNCF or the Bahn, since the ICE doesn't stop anywhere between Strasbourg and Karlsruhe. So, if you want to do Strasbourg to Karlsruhe with the ICE, you need to buy a ticket for the ICE from Strasbourg to Karlsruhe. An ICE ticket from the Bahn for Strasbourg to Karlsruhe is: advance purchase, non-refundable SuperSparPreis, ala 29€; advance purchase, partially refundable SparPreis, ala 23,90€; fully flexible, standard fare, 29,-€.
Alternatively, since your German Rail Pass will cover travel from Kehl to Offenburg or Kehl to Karlsruhe, all you need is a regional ticket from Strasbourg to Kehl, and use the GRP from there. The regional train (SWE) from Strasbourg to Kehl only goes as far as Offenburg, not to Karlsruhe. In Offenburg, you can either take another regional train to Karlsruhe or catch one of the ICEs coming up from Basel to Karlsruhe, which stop in Offenburg, either way with your GRP.
It was over 30 years ago, but I twice bought a regional ticket for the route from Strasbourg to Offenburg, which goes through Kehl. I feel certain that a ticket from Strasbourg to Kehl would have been available then.