Caron shape in Czech and Slovak

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Save for calling it "carka" you are correct. Slovak texts always prefer 
the "apostrophe" form for d, t, l, and L. We only use the other form 
(the one that looks like a raised v) when we use typewriters that do not 
have the "apostrophe" form but do have the caron, or when we write by 
hand (it somehow seems easier to write the little v than the "apostrophe"). 
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Refference:
Letters d L l and t with caron
http://unicode.org/mail-arch/unicode-ml/y2001-m10/0328.html
Omniglot
http://www.omniglot.com/writing/slovak.htm