HREE enrichment (i.e. slope up towards the HREE) can result from many minerals, with some examples being garnet, zircon, xenotime, and more.
Usually HREE depletion (slope down towards the HREE) in igneous rocks (including but not limited to granites) indicates that garnet either exists at source, or has fractionated. Because HREE prefer garnet, and the garnet is left behind, no much HREE is left for the new rock.
This is a very simplified way to look at things and as always there are complications. But it's a good starting point.
According to me Granites as a whole are usually(most of the cases) more enriched in LREE as compared to HREE so if a granite sample is relatively enriched in HREE it can be due to the presence of Garnet(s) since garnets are enriched in HREE.
It's true. During partial melting or crystal-melt fractionation, REE is generally incompatible. I.e., they prefer the melt phase. However, when garnet is in equilibrium with the partial melt (deep C Crust and depths over about 100 km in the mantle) the HREE become compatible with Grt and depleted in the residual melt. Therefore, the rock derived from the residual silicate melt would be depleted in HREE, which is unequivocally seen in the chondrite normalized REE plot. Though Garnet concentrates the HREE more than any other minerals, note that there are other minerals like pyroxene, sphene, and hornblende to which HREE is compatible (the HREE preferentially substitutes with cation in these minerals following Goldsmith's rule).