Analyzing the optical pumping on the <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mn>5</mml:mn> <mml:mi>s</mml:mi> <mml:mn>4</mml:mn> <mml:mi>d</mml:mi> <mml:mrow/> <mml:mmultiscripts> <mml:mi>D</mml:mi> <mml:mn>2</mml:mn

We explore the efficacy of optical pumping on the $5s4d\phantom{\rule{0.16em}{0ex}}^{1}D_{2}\text{\ensuremath{-}}5s8p\phantom{\rule{0.16em}{0ex}}^{1}P_{1}$ $(448\phantom{\rule{0.16em}{0ex}}\mathrm{nm})$ transition in a magneto-optical trap (MOT) of Sr atoms. The number of trapped atoms is enhanced by a factor of $12.0(6)$ relative to the case without repumping light, which is six times as large as that obtained using the pumping transition $5s4d\phantom{\rule{0.16em}{0ex}}^{1}D_{2}\text{\ensuremath{-}}5s6p\phantom{\rule{0.16em}{0ex}}^{1}P_{1}$ $(717\phantom{\rule{0.16em}{0ex}}\mathrm{nm})$. This enhancement is limited by decay pathways that bypass the $5s4d\phantom{\rule{0.16em}{0ex}}^{1}D_{2}$ state, namely $5s5p\phantom{\rule{0.16em}{0ex}}^{1}P_{1}\ensuremath{\rightarrow}5s4d\phantom{\rule{0.16em}{0ex}}^{3}D_{1}\ensuremath{\rightarrow}5s5p\phantom{\rule{0.16em}{0ex}}^{3}P_{0}$ and $5s5p\phantom{\rule{0.16em}{0ex}}^{1}P_{1}\ensuremath{\rightarrow}5s4d\phantom{\rule{0.16em}{0ex}}^{3}D_{2}\ensuremath{\rightarrow}5s5p\phantom{\rule{0.16em}{0ex}}^{3}P_{2}$, which account for 8% of the total loss of the trapped atoms. We determine the decay rates for the $5s5p\phantom{\rule{0.16em}{0ex}}^{1}P_{1}\ensuremath{\rightarrow}5s4d\phantom{\rule{0.16em}{0ex}}^{3}D_{1}$ and $5s5p\phantom{\rule{0.16em}{0ex}}^{1}P_{1}\ensuremath{\rightarrow}5s4d\phantom{\rule{0.16em}{0ex}}^{3}D_{2}$ transitions to be $66(6)\phantom{\rule{0.16em}{0ex}}{\mathrm{s}}^{\ensuremath{-}1}$ and $2.4(2)\ifmmode\times\else\texttimes\fi{}{10}^{2}\phantom{\rule{0.16em}{0ex}}{\mathrm{s}}^{\ensuremath{-}1}$, respectively. Furthermore, we experimentally demonstrate, when the trap beam diameter is small, escape of atoms in the $5s4d\phantom{\rule{0.16em}{0ex}}^{1}D_{2}$ state, which has a relatively long lifetime of $400\phantom{\rule{0.16em}{0ex}}\textmu{}\mathrm{s}$, becomes a dominant loss mechanism, and that the $448\phantom{\rule{0.16em}{0ex}}\mathrm{nm}$ pumping light effectively suppresses this escape. Our findings will contribute to improved laser cooling and fluorescence imaging in cold strontium atom platforms, such as quantum computers based on optical tweezer arrays.