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After replacing

group_delay_spec(omega) = gds(str_GroupDelaySpec)


group_delay_spec = gds(str_GroupDelaySpec)

the above worked for me, the Tkinter input box was opened, i typed omega + 5/2 inside and pressed the run button. Results in the sage console launching the Tk box:

omega + 5/2
<type 'str'>
omega + 5/2
<type 'sage.rings.polynomial.polynomial_rational_flint.Polynomial_rational_flint'>

Inside of the Tk-function there is no way to "preparse" the "function" group_delay_spec(omega) (depending on no omega in fact), the left side in group_delay_spec(omega) = gds(str_GroupDelaySpec) must have a sense "as is". If a function is really needed, the the lambda definition or a clear def block should work.