You really can not beat the old MIT rad lab series when it comes to moding filters, best check there.
Brute force mode filters short out the E-field, orthoganal to the desired mode E-field. others can use lossy materal parallel.
My initial guess, I have none of the reference materials at hand, But TM01 has a circular E-field, bessel functioned.
Insert a printed circuit, low ER, with thin printed copper circles, that correspond to the peak of J01 function.
If neccessary, l/4 matching can be incorporated to lower the TE insertion loss.