1. A computer program product for dynamically adjusting a hover grace period interval, the computer program product comprising a computer readable storage medium having program instructions embodied therewith, the program instructions readable to cause: a processor to display a graphic user interface (GUI) by the processor manipulating pixels upon a screen; the processor to set a default initial static hover grace period interval; the processor to display an initial hover section in the GUI as a result of receiving an initial manipulation of a first hover object displayed in the GUI, following the lapse of the default initial static hover grace period; the processor to track ensuing manipulations of the GUI following the display of the initial hover section and maintain a dynamic hover grace period interval, in order to reduce clutter of displayed hover sections in the GUI, by increasing the dynamic hover grace period interval from the default initial static hover grace period interval when the processor determines that the display of the initial hover section in the GUI was in error and invasive due to the initial hover section obscuring at least a portion of the GUI, wherein the processor sets a first instance of the dynamic hover grace period interval as the default initial static hover grace period interval plus a first time period when the processor tracks a first ensuing GUI manipulation to move the GUI cursor from inside of the displayed initial hover section to outside of the displayed initial hover section, wherein the processor sets a second instance of the dynamic hover grace period interval as the first dynamic hover grace period interval plus a second time period when the processor tracks a second ensuing GUI manipulation to close the displayed initial hover section within a predetermined close hover section time threshold from the display of the initial hover section, wherein the processor sets a third instance of the dynamic hover grace period interval as the second dynamic hover grace period interval plus a third time period when the processor tracks a third ensuing GUI manipulation to move the GUI cursor above a velocity threshold, and wherein the first time period equals the second time period; the processor to further track ensuing manipulations of the GUI following the display of the initial hover section and further maintain the dynamic hover grace period interval by decreasing the dynamic hover grace period interval when the processor detects a threshold number of dynamic hover grace period interval decrease events, wherein the dynamic hover grace period interval decrease events comprise: detecting multiple successive displays of the initial hover section in the GUI within a predetermined same hover section successive display time threshold; detecting a lapse of a predetermined decrease grace period time threshold since a most recent decrease of the dynamic hover grace period interval without an intervening increase of the dynamic hover grace period interval from the most recent decrease and the detecting of the lapse; receiving a GUI deactivation manipulation of the GUI that deactivates the GUI; and displaying a different hover section-from the initial hover section in the GUI within a predetermined different hover section display time threshold from the display of the initial hover section; the processor to receive a subsequent manipulation of a subsequent hover object; the processor to determine a current dynamic hover grace period interval; and the processor to display a subsequent hover section associated with the subsequent hover object following the lapse of the current dynamic hover grace period interval.