As I understand it, the markings of these shevas follow the rules given by R' Shlomo Zalman Hanau, an important 18th-century grammarian. In his system, every sheva following a tenuah kallah (a "light" vowel, i.e., one that substitutes for a sheva or a chataf vowel) is vocalized; examples include מַלְכֵי (since the independent form is מְלָכִים) and נֶעֶרְמוּ (since the singular is נֶעֱרַם). In your example, then, the patach under the כ is presumably a tenuah kallah, since this prefix usually takes a sheva.
By contrast, most other siddurim, such as Artscroll, follow the rules given by R' Eliyahu Bachur (16th century) as interpreted by the Vilna Gaon.
Whether these markings belong in the Siddur Tehillas Hashem is another issue altogether. They're there basically for historical reasons: the old Tehillas Hashem siddur (first published in 1945) was actually mostly a photo-offset of Siddur Seder Ha'avodah, first published in Vilna in 1911, which had them. The printers of the latter siddur seem to have freely tinkered with the wording of both the halachos and the prayers themselves (possibly under the influence of siddurim of other nuschaos); the sheva markings are their addition too. (The original siddur of the Baal HaTanya, and editions such as Torah Ohr that try to reflect it faithfully, don't have such markings.) When the Siddur Tehillas Hashem was re-typeset a few years ago (the edition that you linked to), arguments were made pro and con, but ultimately the editors decided to leave well enough alone.
(I can claim some familiarity with the whole issue, having been one of the proofreaders of that siddur.)