Would this one-liner suffice ?:

>perl -ane "next if $seen{$F[1].$F[2]}++;print" InputFile.txt
----------------------------------------------------------------------
+-------------
  Pos          HLA         Peptide       Core Of Gp Gl Ip Il        Ic
+ore        Identity   Score Aff(nM)   %Rank  BindLevel
  117  HLA-A*11:01       YVNVNMGLK  YVNVNMGLK  0  0  0  0  0    YVNVNM
+GLK GQ924620_HBe_C_ 0.62268    59.3    0.40 <= SB
   28  HLA-A*11:01       WGMDIDPYK  WGMDIDPYK  0  0  0  0  0    WGMDID
+PYK GQ924620_HBe_C_ 0.44617   400.4    1.60 <= WB
  133  HLA-A*11:01       HISCLTFGR  HISCLTFGR  0  0  0  0  0    HISCLT
+FGR GQ924620_HBe_C_ 0.43660   444.0    1.70 <= WB
   47  HLA-A*02:05       YVNVNMGLK  FLPSDFFPS  0  0  0  0  0    FLPSDF
+FPS X02763_HBe_A_po 0.77090    11.9    0.08 <= SB
   40  HLA-A*02:05       ATVELLSFL  ATVELLSFL  0  0  0  0  0    ATVELL
+SFL X02763_HBe_A_po 0.75279    14.5    0.10 <= SB
    1  HLA-A*02:05       MQLFHLCLI  MQLFHLCLI  0  0  0  0  0    MQLFHL
+CLI X02763_HBe_A_po 0.66669    36.8    0.30 <= SB
    9  HLA-A*02:05       IISCTCPTV  IISCTCPTV  0  0  0  0  0    IISCTC
+PTV X02763_HBe_A_po 0.52206   176.1    1.40 <= WB
  147  HLA-A*02:05       YLVSFGVWI  YLVSFGVWI  0  0  0  0  0    YLVSFG
+VWI X02763_HBe_A_po 0.51724   185.5    1.40 <= WB
   55  HLA-A*02:05       SVRDLLDTA  SVRDLLDTA  0  0  0  0  0    SVRDLL
+DTA X02763_HBe_A_po 0.49966   224.4    1.70 <= WB
  114  HLA-A*02:05       VVNYVNTNV  VVNYVNTNV  0  0  0  0  0    VVNYVN
+TNV X02763_HBe_A_po 0.48729   256.6    1.80 <= WB
   93  HLA-A*02:05       ELMTLATWV  ELMTLATWV  0  0  0  0  0    ELMTLA
+TWV X02763_HBe_A_po 0.46686   320.0    2.50
    8  HLA-A*02:05       LIISCTCPT  LIISCTCPT  0  0  0  0  0    LIISCT
+CPT X02763_HBe_A_po 0.45053   381.9    2.50
  117  HLA-A*11:01       IISCTCPTV  YVNVNMGLK  0  0  0  0  0    YVNVNM
+GLK AB219428_HBe_B_ 0.62268    59.3    0.40 <= SB
[download]

UPDATE: If you want to maintain the headers, try this:

perl  -ane "next unless not $seen{$F[1].$F[2]}++ or m/^\s*\D/;print" I
+nputFile.txt
[download]