One cannot of course directly compare these bounds to cosmic strings in TGD sense (not gauge theory strings but primordial 4-D string like objects). In TGD framework the string tension characterizes the density of Kähler magnetic energy of 4-D string like object with 2-D string world sheet as Minkowski space projection.
Cosmic string tension is inversely proportional to the square of CP2 length scale R and to Kähler coupling strength αK for which the most recent estimate is as equal to fine structure constant: αK≈ 1/137. The value of R is fixed by p-adic mass calculations from the conditions that electron mass comes out correctly. The velocity spectrum of distance stars in galaxy gives the same estimate if the gravitational field created by long cosmic string along which galaxies are located like pearls in string, gives an estimate consistent with this value. The estimate of cosmic string tension is TG= 6.9× 10-7 and is therefore in the interval 10-6-10-7 , where the upper bounds for other string tensions reside.
A comparison with string theory is in order. For Nambu-Goto strings the estimated upper bound for string tension is GT<1.5× 10-7 - not a good news since the Nambu-Goto string tension should satisfy GT=1 in the original approach. The same holds true also for superstrings in the original sense of the word. Therefore the situation is not very promising for superstrings. In fact, it turned out very difficult to find anything concrete about the string tension of superstrings. I however found from web a ten year old estimate estimate TG= 1/3000 for superstring tension involving experimental input. Presumably the Planck 2013 results would lower this estimate by few orders of magnitude.
For background see the chapter Cosmic Strings of "Physics in Many-Sheeted Space-time".