I only know of Nuclease-Free Water, which may work as a substitute for TE. Just make sure you minimize repeated freeze-thaw cycles, since it may degrade your DNA.
Hi, IDT actually gives advice on how to resuspend them: https://www.idtdna.com/pages/education/decoded/article/tips-for-working-with-gblocks-gene-fragments. Main issue is adherence to plastic at low concentrations.
I'd add in that you should dilute & aliquot into "single use portions". That way you aren't doing repeated freeze-thaw cycles. And keep in a deep freeze or non-frost-free freezer.