You can't do it with regex, but you can do it with RENAME wildcards.
ren "c:\backup\t1-??-?? t2-??-??.txt" "???00-99*"
Within the target mask, each ?
preserves one character, and the literals do a one for one character replacement, and the *
preserves the remainder.
See How does the Windows RENAME command interpret wildcards? for more info.
If you are worried that the source mask is not specific enough, then you could use the following batch script to guarantee only properly named files are renamed.
pushd "c:\backup"
for /f "delims=" %%F in (
'dir /b /a-d "t1-??-?? t2-??-??.txt" ^| findstr /xirc:"t1-[0-9][0-9]-[0-9][0-9] t2-[0-9][0-9]-[0-9][0-9].txt"'
) do ren "%%F" "???00-99*"
popd
But your powershell script is probably easier :-)