RSA Key generation Public exponent too big
The $2^{16} + 1$ exponent is really meant for use in real life systems, in which public keys are expected to be considerably larger than that. I guess CrypTool assumes this is the case, as you would expect, really.

That said, if $\gcd{(e, \varphi{(n)})} = 1$, then $gcd{(e ~ \mathrm{mod} ~ \varphi{(n)}, \varphi{(n)})} = 1$ by definition, so such an $e$ will still work regardless, as noted by fgrieu in the comments.