Looks weired but a sound of C and T has to be somehow connected, at least it feels like they are to me. Based on my experience, sound of Polish Ć and Czech Ť are transitional between Polish/Czech T/C. Proper linguist might put some more light on it than just my speculation.
Our C is reffered in IPA as joined “TS” sound, so there is definitely some merit to that
Polish C is also described as /t͡s/ (e.g. co /t͡sɔ/). According to wiki both are dental and voiceless although one is plosive and the other affricate. As I’ve read their descriptions on wiki, they made a lot of sense - /t͡s/ starts with a blockade of airway (just as /t/) but the air is released slightly differently thus making the difference in sound produced.